Harmonic Oscillator Homework: Issues with d)

AI Thread Summary
The discussion focuses on solving a harmonic oscillator problem, specifically addressing the challenges with part d. The amplitude, maximum velocity, and period calculations in parts a, b, and c are confirmed to be correct. For part d, the equilibrium position occurs when the cosine function equals zero, which can be achieved by setting the argument to π/2 or 3π/2. The solution for the first instance yields specific times, and the pattern continues every half period thereafter. Understanding the periodic nature of the cosine function is crucial for determining the equilibrium positions.
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Homework Statement



I am having issues with d) and would like to know if I did the a, b, and c correctly. I have tried to look online for explanation but with no success.

A harmonic oscillator executes motion according to the equation x=(12.4cm)cos( (34.4 rad /s)t+ π/5 ) .

a) Determine the amplitude of the oscillation.
b) Determine the maximum velocity of the oscillation.
c) Determine the period of the oscillation.
d) Determine when the object is at its equilibrium position.

Homework Equations


max v=Aw
T=1/f

The Attempt at a Solution


a) Determine the amplitude of the oscillation.

Amplitude would just be 12.4cm, we can take it straight out from the equation.

b) Determine the maximum velocity of the oscillation.

max v=Aw=0.124m*34.4rad/s=4.27m/s

c) Determine the period of the oscillation.

Here we know that 2π rad is one turn so 34.4 rad is 5.48 turns.
So we have 5.48 turns per second.

T=1/f=1/5.48=0.183secs

d) Determine when the object is at its equilibrium position.

I know that the object is in equilibrium when x=0, so
0=(12.4cm)cos( (34.4 rad /s)t+ π/5 )

I may be missing some algebra skills, but I even try to compute it online and it wields no solution. What am I doing wrong?
 
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Your work on parts (a) through (c) looks fine.

For part (d), consider what the argument of the cosine function needs to be for the cosine to be zero. (Hint: there are many such angles)
 
So cos( (34.4 rad /s)t+ π/5 ) need to equal 0?

(34.4rad/s)t+π/5 has to be equal to π/2 or 3π/2?
 
That is going to wield t= 0.02739s and 0.1187s, does not feel right though because a period takes 0.183secs.
 
alex91alex91alex said:
So cos( (34.4 rad /s)t+ π/5 ) need to equal 0?

(34.4rad/s)t+π/5 has to be equal to π/2 or 3π/2?
Yes.

In fact, the cosine will be zero every time its argument is equivalent to π/2 or 3π/2. You should be able to write it as a function of n, where n = 0,1,2,... Or you can solve for the first instance (n = 0 so that the argument is π/2) and then it will happen every half period after that.
 
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