# Harmonic motion problem

#### coooool222

##### New member
I really need help my teacher never taught us this and assign this for us .

Spring Motion The height attained by a weight attached to a spring set in motion is
s(t)=−4cos8πts(t)=−4cos⁡8πt inches after t seconds.
(a) Find the maximum height that the weight rises above the equilibrium position y = 0
(b) When does the weight first reach its maximum height if t≥0?
(c) What are the frequency and the period?

i know A is 4 since the frequency is 4

I have no clue for B

Frequncy is 4 and the period is 1/4 = 2 pi / 8 pi = 1/4

#### Otis

##### Elite Member
s(t)=−4cos8πts(t)=−4cos⁡8πt
Hi. Will you please retype the expression for function s using function notation?

Why does symbol s appear within the definition for function s?

You also say that −4cos8πts(t) = −4cos⁡8πt. That doesn't seem right.

#### topsquark

##### Senior Member
I really need help my teacher never taught us this and assign this for us .

Spring Motion The height attained by a weight attached to a spring set in motion is
s(t)=−4cos8πts(t)=−4cos⁡8πt inches after t seconds.
(a) Find the maximum height that the weight rises above the equilibrium position y = 0
(b) When does the weight first reach its maximum height if t≥0?
(c) What are the frequency and the period?

i know A is 4 since the frequency is 4

I have no clue for B

Frequncy is 4 and the period is 1/4 = 2 pi / 8 pi = 1/4
Perhaps you have some source material to read? Perhaps one such that will tell you that the amplitude is 4 inches, not the frequency. See here. (Actually, f = 4 Hz, but that's not what you were looking for in a).) The general form is [imath]s(t) = A ~ cos( 2 \pi ft + \phi)[/imath] where A is the amplitude, f is the frequency, and [imath]\phi[/imath] is the phase shift.

[imath]s(t) = -4 ~ cos( 8 \pi t )[/imath]

The phase shift is 0 and A is negative so at t = 0 the cosine function is at it's minimum so we have to go 1/2 a wavelength to get to a maximum. What is the wavelength? That will tell you when s(t) gets to max height.

Give it another try.

-Dan