DuckieDai Hooke's Law and Elastic Energy Python Program

physics · MIT License

Overview

Solve spring force, spring constant, displacement, or elastic potential energy with Hooke's law and PE = 0.5*k*x^2.

Tested on a TI calculator
Downloaded 38 times
Version 1.0.0
7070 bytes
Uses math

Download HOOKELAW.py Read the source How to install

Before you run it

TI-84 Plus CE Python · tested on OS 5.8.3, Python App 5.8.3.0048
TI Connect CE .py conversion to a Python AppVar in RAM; physically verified one program at a time
The spring behaves linearly within its elastic range.
Spring constant must be positive and divisor values cannot be zero.
Hooke's law is inaccurate beyond the spring's elastic limit.

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Learn the math

How Hooke's law and spring energy work

The idea

A spring pushes back harder the further you stretch or squeeze it. For an ideal spring the force is proportional to the displacement, and the constant of proportionality is the spring constant k.

A stretched or compressed spring also stores energy, which grows with the square of the displacement.

The formula

Fs = -k*x

PE = 0.5*k*x^2

Fs: spring force (N)
k: spring constant (N/m)
x: displacement from the rest position (m)
PE: elastic potential energy (J)

Using the program

Choices 1 to 3 use the force formula: spring force, spring constant from force, displacement from force.
Choices 4 to 6 use the energy formula: elastic PE, spring constant from PE, displacement from PE.
The menu is two screens long. Press Enter to see choices 4 to 6.

Worked example

A spring with k = 200 N/m is stretched 0.05 m. Choose 1 and enter 200 and 0.05.

The program shows Fs = -10.0 newtons. The minus sign means the spring pulls back, opposite to the stretch.

Choosing 4 with the same numbers gives PE = 0.25 joules (the program prints 0.25000000000000006, a rounding artifact).

Tips and common mistakes

Convert centimeters to meters: 5 cm is 0.05 m.
The minus sign shows direction. Many problems only want the size of the force.
Energy depends on x squared, so doubling the stretch stores four times the energy.

Where this comes up

Springs appear in the forces and energy units of physics and again in simple harmonic motion. Lab courses use the law to find a spring constant from a force and stretch graph.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Springs for TI-84 Plus CE Python."""

from math import sqrt


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def number(prompt):
    """Allow positive, negative, or zero values."""
    while True:
        try:
            value = float(input(prompt))

            if value > -1e100 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a valid number.")


def nonzero_number(prompt):
    """Require a number other than zero."""
    while True:
        value = number(prompt)

        if value != 0:
            return value

        print("Value cannot be zero.")


def positive_number(prompt):
    """Require a value greater than zero."""
    while True:
        try:
            value = float(input(prompt))

            if value > 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a number above 0.")


def nonnegative_number(prompt):
    """Allow zero or positive values."""
    while True:
        try:
            value = float(input(prompt))

            if value >= 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter 0 or greater.")


def show_answer(name, value, unit):
    input("Press enter for answer ")
    print("\n" * 6)
    print("ANSWER")
    print(name + " = " + str(value))
    print(unit)


def main():
    duckiedai_intro("SPRING ENERGY")

    print("HOOKE'S LAW")
    print("& ELASTIC ENERGY")
    print()
    print("Fs = -k*x")
    print("PE = 0.5*k*x^2")
    input("Press enter for menu ")
    print("\n" * 6)
    print()
    print("What do you need?")
    print()
    print("1. Spring force")
    print("2. Spring constant")
    print("   from force")
    print("3. Displacement")
    print("   from force")
    input("Press enter for more ")
    print("\n" * 6)
    print("4. Elastic PE")
    print("5. Spring constant")
    print("   from PE")
    print("6. Displacement")
    print("   from PE")
    print()

    choice = input("Choose 1-6: ")

    print()

    # ==========================================
    # 1. SPRING FORCE
    #
    # Fs = -k*x
    # ==========================================

    if choice == "1":

        k = positive_number("k (N/m): ")
        x = number("Displacement (m): ")

        force = -k * x

        print()
        print("Using:")
        print("Fs = -k*x")
        print()
        print("Fs = -" + str(k))
        print("x " + str(x))

        show_answer(
            "Fs",
            force,
            "newtons"
        )

        print()
        print("Minus sign means")
        print("restoring force is")
        print("opposite displacement.")


    # ==========================================
    # 2. SPRING CONSTANT FROM FORCE
    #
    # k = -Fs/x
    # ==========================================

    elif choice == "2":

        force = number("Spring force (N): ")
        x = nonzero_number("Displacement (m): ")

        k = -force / x

        print()
        print("Using:")
        print("Fs = -k*x")
        print()
        print("Rearranged:")
        print("k = -Fs/x")

        if k <= 0:

            print()
            print("Result gives k <= 0.")
            print("Check force and")
            print("direction signs.")

        else:

            show_answer(
                "k",
                k,
                "N/m"
            )


    # ==========================================
    # 3. DISPLACEMENT FROM FORCE
    #
    # x = -Fs/k
    # ==========================================

    elif choice == "3":

        force = number("Spring force (N): ")
        k = positive_number("k (N/m): ")

        x = -force / k

        print()
        print("Using:")
        print("Fs = -k*x")
        print()
        print("Rearranged:")
        print("x = -Fs/k")

        show_answer(
            "x",
            x,
            "meters"
        )


    # ==========================================
    # 4. ELASTIC POTENTIAL ENERGY
    #
    # PE = 0.5*k*x^2
    # ==========================================

    elif choice == "4":

        k = positive_number("k (N/m): ")
        x = number("Displacement (m): ")

        pe = (
            0.5 *
            k *
            x ** 2
        )

        print()
        print("Using:")
        print("PE = 0.5*k*x^2")
        print()
        print("PE = 0.5 x")
        print(str(k) + " x")
        print(str(x) + "^2")

        show_answer(
            "PE",
            pe,
            "joules"
        )


    # ==========================================
    # 5. SPRING CONSTANT FROM ENERGY
    #
    # k = 2*PE/x^2
    # ==========================================

    elif choice == "5":

        pe = nonnegative_number("Elastic PE (J): ")
        x = nonzero_number("Displacement (m): ")

        k = (
            2 * pe /
            (x ** 2)
        )

        print()
        print("Using:")
        print("PE = 0.5*k*x^2")
        print()
        print("Rearranged:")
        print("k = 2*PE/x^2")

        show_answer(
            "k",
            k,
            "N/m"
        )


    # ==========================================
    # 6. DISPLACEMENT FROM ENERGY
    #
    # x = +/- sqrt(2*PE/k)
    # ==========================================

    elif choice == "6":

        pe = nonnegative_number("Elastic PE (J): ")
        k = positive_number("k (N/m): ")

        x = sqrt(
            (2 * pe) / k
        )

        print()
        print("Using:")
        print("PE = 0.5*k*x^2")
        print()
        print("Rearranged:")
        print("x = +/-sqrt(2*PE/k)")
        print()
        input("Press enter for answer ")
        print("\n" * 6)
        print("ANSWER")
        print("|x| = " + str(x))
        print("meters")
        print()
        print("Possible positions:")
        print("x = " + str(x))
        print("or")
        print("x = -" + str(x))

    else:
        print("Invalid choice.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Springs for TI-84 Plus CE Python."""
from math import sqrt
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def number(prompt):
"""Allow positive, negative, or zero values."""
while True:
try:
value = float(input(prompt))
if value > -1e100 and value < 1e100:
return value
except ValueError:
pass
print("Enter a valid number.")
def nonzero_number(prompt):
"""Require a number other than zero."""
while True:
value = number(prompt)
if value != 0:
return value
print("Value cannot be zero.")
def positive_number(prompt):
"""Require a value greater than zero."""
while True:
try:
value = float(input(prompt))
if value > 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter a number above 0.")
def nonnegative_number(prompt):
"""Allow zero or positive values."""
while True:
try:
value = float(input(prompt))
if value >= 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter 0 or greater.")
def show_answer(name, value, unit):
input("Press enter for answer ")
print("\n" * 6)
print("ANSWER")
print(name + " = " + str(value))
print(unit)
def main():
duckiedai_intro("SPRING ENERGY")
print("HOOKE'S LAW")
print("& ELASTIC ENERGY")
print()
print("Fs = -k*x")
print("PE = 0.5*k*x^2")
input("Press enter for menu ")
print("\n" * 6)
print()
print("What do you need?")
print()
print("1. Spring force")
print("2. Spring constant")
print(" from force")
print("3. Displacement")
print(" from force")
input("Press enter for more ")
print("\n" * 6)
print("4. Elastic PE")
print("5. Spring constant")
print(" from PE")
print("6. Displacement")
print(" from PE")
print()
choice = input("Choose 1-6: ")
print()
# ==========================================
# 1. SPRING FORCE
#
# Fs = -k*x
# ==========================================
if choice == "1":
k = positive_number("k (N/m): ")
x = number("Displacement (m): ")
force = -k * x
print()
print("Using:")
print("Fs = -k*x")
print()
print("Fs = -" + str(k))
print("x " + str(x))
show_answer(
"Fs",
force,
"newtons"
)
print()
print("Minus sign means")
print("restoring force is")
print("opposite displacement.")
# ==========================================
# 2. SPRING CONSTANT FROM FORCE
#
# k = -Fs/x
# ==========================================
elif choice == "2":
force = number("Spring force (N): ")
x = nonzero_number("Displacement (m): ")
k = -force / x
print()
print("Using:")
print("Fs = -k*x")
print()
print("Rearranged:")
print("k = -Fs/x")
if k <= 0:
print()
print("Result gives k <= 0.")
print("Check force and")
print("direction signs.")
else:
show_answer(
"k",
k,
"N/m"
)
# ==========================================
# 3. DISPLACEMENT FROM FORCE
#
# x = -Fs/k
# ==========================================
elif choice == "3":
force = number("Spring force (N): ")
k = positive_number("k (N/m): ")
x = -force / k
print()
print("Using:")
print("Fs = -k*x")
print()
print("Rearranged:")
print("x = -Fs/k")
show_answer(
"x",
x,
"meters"
)
# ==========================================
# 4. ELASTIC POTENTIAL ENERGY
#
# PE = 0.5*k*x^2
# ==========================================
elif choice == "4":
k = positive_number("k (N/m): ")
x = number("Displacement (m): ")
pe = (
0.5 *
k *
x ** 2
)
print()
print("Using:")
print("PE = 0.5*k*x^2")
print()
print("PE = 0.5 x")
print(str(k) + " x")
print(str(x) + "^2")
show_answer(
"PE",
pe,
"joules"
)
# ==========================================
# 5. SPRING CONSTANT FROM ENERGY
#
# k = 2*PE/x^2
# ==========================================
elif choice == "5":
pe = nonnegative_number("Elastic PE (J): ")
x = nonzero_number("Displacement (m): ")
k = (
2 * pe /
(x ** 2)
)
print()
print("Using:")
print("PE = 0.5*k*x^2")
print()
print("Rearranged:")
print("k = 2*PE/x^2")
show_answer(
"k",
k,
"N/m"
)
# ==========================================
# 6. DISPLACEMENT FROM ENERGY
#
# x = +/- sqrt(2*PE/k)
# ==========================================
elif choice == "6":
pe = nonnegative_number("Elastic PE (J): ")
k = positive_number("k (N/m): ")
x = sqrt(
(2 * pe) / k
)
print()
print("Using:")
print("PE = 0.5*k*x^2")
print()
print("Rearranged:")
print("x = +/-sqrt(2*PE/k)")
print()
input("Press enter for answer ")
print("\n" * 6)
print("ANSWER")
print("|x| = " + str(x))
print("meters")
print()
print("Possible positions:")
print("x = " + str(x))
print("or")
print("x = -" + str(x))
else:
print("Invalid choice.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: HOOKELAW.py
Size: 7070 bytes
SHA-256: 12c4705772c67397d3761f1be5252249edfc811ffd6f11985993b7b9e1473a48

Usage

Inputs

Requested spring quantity
Known force, displacement, spring constant, or elastic energy as required

Outputs

Requested spring value, including both possible displacement signs when solving from energy

Units: Use newtons, metres, newtons per metre, and joules consistently.

Assumptions and limitations

Assumptions

The spring behaves linearly within its elastic range.

Constraints

Spring constant must be positive and divisor values cannot be zero.

Known failures

Hooke's law is inaccurate beyond the spring's elastic limit.
Force and displacement signs must follow one consistent direction convention.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact paginated .py transferred through TI Connect CE into RAM and tested individually
What happened: Passed: branded intro, multi page spring menu, Hooke law and elastic energy workflows, and answer screens ran on the physical calculator
Dependencies: math
Suggested calculator name: HOOKELAW — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as HOOKELAW or another name, then open the Python App and try the worked example on this page first.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-09-23. Download this reviewed version

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