# Homework Help: Simple Harmonic Motion and phase constant

1. Jul 25, 2015

### Dalip Saini

A simple harmonic oscillator consists of a block of mass 45 g attached to a spring of spring constant 240 N/m, oscillating on a frictionless surface. If the block is displaced 3.5 cm from its equilibrium position and released so that its initial velocity is zero, what is the phase constant, φ , of its oscillations? Assume the block moves according to the equation x=xmaxcos(ωt+φ) .
• A :

45o

• B :

30o

• C :

0o

• D :

90o

• E :

The phase constant is arbitrary.

2. Jul 25, 2015

### jbriggs444

What do you think?

3. Jul 25, 2015

### Dalip Saini

Im really stuck on how to solve this problem. I know that the Xm is 0.035m. I also know that the w can be solved for using sqroot(k/m). But I'm stuck now on how to use this information to solve for the answer

4. Jul 25, 2015

### jbriggs444

You should not need to do any arithmetic to answer this problem. You are not asked for omega.

Assume that "initial" means t = 0. What is the situation at t=0?

5. Jul 25, 2015

### Dalip Saini

since the initial velocity is zero, would u take the derivative of the function to get v=-wxmsin(wt+φ). Then plug in the values to get 0 = -240(0.035)sin[(240)(0)+φ). Then solve for φ and get zero. According to the assignment the correct answer is zero. Is this the correct way to solve it?

6. Jul 25, 2015

### jbriggs444

Yes, that is one correct way.

Another approach would be to convince yourself that the starting position is a position of maximum displacement and that the cosine function is maximized when its argument is zero.

7. Jul 25, 2015

ok thank you