Calculating Time for Simple Harmonic Motion

[Mdhiggenz]

Homework Statement

An object is undergoing simple harmonic motion with frequency = 3.2 Hz and amplitude = 0.12 m. At = 0 the object is at = 0. How long does it take the object to go from = 0 to = 7.2×10−2 m?

Homework Equations

The Attempt at a Solution

s(t)=Asin(ωt)

A=amplitude=.12 m
ω=2πf=2π*3.2=20.1
t=undefined
s(t)=.12sin(20.1)
7.2*10^-2=.12sin(20.1t) divide out the .12
.6=sin(20.1t) Take the inverse sin of both sides
arcsin.6=20.1t The inverse of sin cancels out sin on the right so 20.1t is left.
36.87=20.1t Divide out 47.75 to get t.
t=1.8338 seconds

They want the answer in two figs, I put 1.8, and they marked it wrong are my steps wrong?

 

[Andrew Mason]

s(t)=Asin(ωt)

A=amplitude=.12 m
ω=2πf=2π*3.2=20.1
t=undefined
s(t)=.12sin(20.1)
7.2*10^-2=.12sin(20.1t) divide out the .12
.6=sin(20.1t) Take the inverse sin of both sides
arcsin.6=20.1t The inverse of sin cancels out sin on the right so 20.1t is left.
36.87=20.1t Divide out 47.75 to get t.
t=1.8338 seconds

They want the answer in two figs, I put 1.8, and they marked it wrong are my steps wrong?

Your method is correct. But watch your units. The arcsin of .6 must be expressed in radians. You are using degrees.

A good way to approach this kind of problem is to estimate it first. You can tell that it will be less than 1/4 of a cycle, and there are 3.2 cycles in one second, so it is a lot less than a second.

AM