Simple Harmonic Motion Simulations: Exploring Force Models with Excel
What did you do in lab 1A with Excel simulation?
You used Excel to make a simulation of a ball of mass m hanging from a vertical spring with spring constant k. Let y0, v0, and a0 represent the position, velocity, and acceleration of the ball at time t0.
What equations were used to calculate the position and velocity a short time later?
You used the equations: i. V1 = v0 + a * dt ii. V1 = y0 + v * dt
Which statements are correct regarding the simulation?
Select all of the following statements that are correct:
o You could test different models for the force acting on the ball by modifying the equation for how a1 was calculated.
o Equation i. assumes the acceleration is approximately constant during the time interval dt.
o Equation ii. assumes the velocity is approximately constant and equal to the final velocity during the time interval dt.
Answer:
The student can test different force models by tweaking the acceleration equation, and both equations provided assume that their variables (Acceleration and Velocity) are constant during the brief time interval, dt. These methods can also be applied in scenarios beyond just simple harmonic motion.
Explanation: In the presented simulation of a ball of mass m hanging from a vertical spring with spring constant k, you are correct in stating that by modifying the equation for how a1 was calculated, you could indeed test different models for the force acting on the ball. Also, it is correct that equation i. V1 = v0 + a * dt assumes the acceleration is approximately constant during the time interval dt. Lastly, equation ii. V1 = y0 + v * dt is indeed assuming that the velocity is approximately constant and equal to the final velocity during the time interval dt. The claim that this method only works for simple harmonic motion, however, is incorrect. While it's certainly applied often in simple harmonic motion scenarios due to their simplicity, similar numerical methods can be used for other types of motion or forces that aren't easily solvable analytically.