Question

An object attached to a coiled spring is pulled down 5 centimeters from its rest position and released. If the motion is simple harmonic in nature, with a period of seconds.

a. What is the maximum displacement form equilibrium of the object?


b. What is the time required for one oscillation?


c. What is the frequency?


d. Write an equation to model the motion of the object.

Answer 1

a.) Note that the maximum displacement is the amount the spring is pulled downwards which is 5 cm.

b.) The time required for one oscillation is the Period. You didn't specify it so we can't really say what it is.

c.) The frequency = 1/Period, i.e. frequency is the reciprocal of the Period.

d.) Since the maximum displacement is 5 cm and the string was pulled downwards to start off with, the amplitude will be 5 and because it starts off downwards, we will have to make the 5 negative hence -5. The appropriate sinusoidal function to use in this case would be cosine. Now inside the brackets of cos( ) we will have 2pi/P, where P is the the period, multiplied by t, which is time. Hence the model is:\[\bf f(t)=-5\cos \left( \frac{2 \pi}{P}t \right)\]

Answer 2

@TruePanda Are you given the period?

Answer 3

Oh yeah sorry. period of pi seconds

Answer 4

Plug in \(\bf \pi\) whereever you see \(\bf P\). Hence the period is now \(\bf \pi \ seconds\).
The frequency is \(\bf 1/\pi \ hertz \) and the model becomes \(\bf f(t)=-5cos(2t)\)

@TruePanda