If you describe the motion of an oscillator with a cosine function x = A cos(wt

Question

If you describe the motion of an oscillator with a cosine function x = A cos(wt + phi), and at t = 0, the oscillator is at the equilibrium point and moving towards the positive x axis, what is the value of phi?

Question 1 options:

0

pi/2

- pi/2

pi

Question 2

If you describe the motion of an oscillator with a sine function x = A sin(wt + phi), and at time t = 0, x = +A, what is the value of phi?

Question 2 options:

0

pi/2

-pi/2

pi

0

pi/2

- pi/2

pi

Question 2

If you describe the motion of an oscillator with a sine function x = A sin(wt + phi), and at time t = 0, x = +A, what is the value of phi?

Question 2 options:

0

pi/2

-pi/2

pi

Explanation / Answer

1. -pi/2

At t=0, x=0 => it should be either cos-pi/2 or cospi/2

But x is positive at t>0,

if it is pi/2 further increase in t, sends it to second quadrant where cosine is negative

if it's -pi/2, further increase in t, it will remain in 4th quadrant where cosine is positive.

2.pi/2. As sin0 =sinpi=0, sin-pi/2 =-1

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