Simple Harmonic Oscillator question

[mossfan563]

Homework Statement

A simple harmonic oscillator consists of a block of mass 2.30 kg attached to a spring of spring constant 440 N/m. When t = 1.70 s, the position and velocity of the block are x = 0.135 m and v = 3.130 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?

Homework Equations

x = x_m*cos(wt + (phi))
v = -w*x_m*sin(wt + (phi))
w = angular frequency = 2*pi*f

The Attempt at a Solution

I tried solving for phi, being the phase constant, so I could eventually find x when t = 0 but I got nowhere. I already got part A correct. How do I approach parts b and c?

 

[alphysicist]

Hi mossfan563,

Homework Statement

A simple harmonic oscillator consists of a block of mass 2.30 kg attached to a spring of spring constant 440 N/m. When t = 1.70 s, the position and velocity of the block are x = 0.135 m and v = 3.130 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?

Homework Equations

x = x_m*cos(wt + (phi))
v = -w*x_m*sin(wt + (phi))
w = angular frequency = 2*pi*f

The Attempt at a Solution

I tried solving for phi, being the phase constant, so I could eventually find x when t = 0

That sounds like the right idea. Can you show how far you got? Did you get a wrong value for phi, or could you not solve for phi from the x and v equation?

 

[mossfan563]

Well, since I already have values for w, x_m, and t, I don't really know how to solve for phi if it were in terms of the variables. Do I use a trig identity to try and solve for phi?

 

[unscientific]

v = $$\pm$$$$\omega$$$$\sqrt{}$$x₀² - x²

omega = sqrt(k/m)

3.10² = (k/m)(x₀² - x²)


3.10² = (440/2.3)(x₀² - 0.135²)


Then, solve for x₀

 

[alphysicist]

Well, since I already have values for w, x_m, and t, I don't really know how to solve for phi if it were in terms of the variables. Do I use a trig identity to try and solve for phi?

To solve for phi that is what I would do. If you plug in your values into the x and v equation you have two equations with two unknowns (x_m and phi).

Use algebra to eliminate x_m, and so get one equation with one unknown. Do you see what to do then?

 

[mossfan563]

I still don't see how you solve for phi when you still have sin (WT + (phi)).

How I solve for just phi when I have something like that?

 

[alphysicist]

I still don't see how you solve for phi when you still have sin (WT + (phi)).

How I solve for just phi when I have something like that?

What equation did you get when you eliminated x_m from the equations?

At that point you should have had only one uknown (phi), but that unknown would be inside two trig function. The general idea is that you could then combine the trig functions into one trig function, and then take its inverse to solve for phi. Is that what you are getting?