The Perodic Motion Spring Problem

[blackbyron]

Homework Statement

A mass 0.82kg is attached to a spring of constant 205N/m. The mass slides along a horizontal frictionless surface. The spring is compressed a distance 12.2cm from its equilibrium position and the mass is released from rest. How long after it is released will the mass be at x=-1cm for the first time?

Homework Equations

x(t) = A*cos($$\omega$$*t+$$\phi$$)
E = (1/2)(k)(A)^2 = (1/2)(k)(x^2) + (1/2)(m)(v^2)

The Attempt at a Solution

I'm having trouble finding out time. I tried to solve for max velocity and solve for regular velocity, but sadly it didn't work.

I also let A = .122m when t = 0.

I know that the equilibrium position is zero, but are they asking me to find out the time between equilibrium position and -1cm? If it is, does that mean, A = -1cm?

Thanks,

I spend hours trying to do some research on it, even I look at my teachers notes.

 

[ehild]

I know that the equilibrium position is zero, but are they asking me to find out the time between equilibrium position and -1cm? If it is, does that mean, A = -1cm?

They ask to calculate the time while the object reaches x=-1 cm from the initial position. A is the amplitude, it is unchanged.


ehild

 

[blackbyron]

They ask to calculate the time while the object reaches x=-1 cm from the initial position. A is the amplitude, it is unchanged.


ehild

Thanks for the reply. Okay, so it basically asks me to find the time that reaches from the initial position. So, do I need to find the displacement, for example, it starts from 0 to 12cm, then 12cm, to -1cm? Do I to add them together so I can solve for t?

 

[blackbyron]

So I tried this,

x(t) = Acos(wt+Q)
x(0) = Acos(w(0)) = .122m -----> A = .122m


set

-.01m = .122cos(w(t)) + Q) Q = 0
-.125m = cos((w(t))

w = sqrt(k/m) = 15.81 rad/s

1.696 = 15.81t

t = .107s

but the answer says its .0942s, so I have no idea how it got that.

 

[ehild]

The vibration starts with x=-0.122 m, as the spring is compressed, (shorter than the equilibrium length). What is the phase constant then?

ehild

 

[blackbyron]

The vibration starts with x=-0.122 m, as the spring is compressed, (shorter than the equilibrium length). What is the phase constant then?

ehild

OOOOHHH, I see, yeah, what am I thinking here? lol


Thank you ehild, sorry for trouble.