Modeling simple harmonic motion. Confirm my answer please.

[redkryp]

Hi, hoping to get confirmation that I have done this problem correctly.

Find a function that models the simple harmonic motion of the given properties:

amplitude = 2.4 meters
frequency = 750 Hz

Assume maximum displacement at time t=0.

Use the form

f(t) = a sin(k(t-c)) + b or
f(t) = a cos(k(t-c)) +b

First, since I am assuming max displacement at t=0, then I need to use the equation involving cosine.

Second, I am only given amp and freq, so c = 0 and b = 0

Third, I know the value of the frequency is the reciprocal value of the period, so the period of this function is 1/750

Fourth, 2pi / k = 1/750

k = 1500pi

So my answer should be: f(t) = 2.4cos((1500pi)(t))

Thanks!

 

[Unknown008]

Well done! =)

 

[redkryp]

Thank you!

 

[burakaltr]

Hi, hoping to get confirmation that I have done this problem correctly.

Find a function that models the simple harmonic motion of the given properties:

amplitude = 2.4 meters
frequency = 750 Hz

Assume maximum displacement at time t=0.

Use the form

f(t) = a sin(k(t-c)) + b or
f(t) = a cos(k(t-c)) +b

First, since I am assuming max displacement at t=0, then I need to use the equation involving cosine.

Second, I am only given amp and freq, so c = 0 and b = 0

Third, I know the value of the frequency is the reciprocal value of the period, so the period of this function is 1/750

Fourth, 2pi / k = 1/750

k = 1500pi

So my answer should be: f(t) = 2.4cos((1500pi)(t))

Thanks!

The harmonic function is in the form

where

A=Amplitude=Max value
T=Period
f=frequency=1/T
w=angular speed=2*PI*f
phi=phase ang le in radians

f(t)=A COS(wt+phi)