DuckieDai Hooke's Law and Elastic Energy Python Program

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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.

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.

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Exact reviewed bytes

Source code

Download .py

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"""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

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Version history

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

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