A mass m=.5kg on a spring with a spring constant. It is displaced by the distance x_max =20cm (.2m) from equilibrium on a frictionless horizontal surface. At the time t=0s the mass is released and it begins to oscillate. Assume that T=3.14s.
Find the following for when t=0, T/4, T/2, 3T/4, and T:
displacement
speed
restoring force (F=kx)
acceleration (a=F/m)
kinetic energy (1/2mv^2)
potential energy (1/2kx^2)
For t=0s I got: .2m, 0m/s, .4N, .8m/s^2, 0J, and .04J respectively. I got this first by finding the spring constant using this equation: T= 2*pi*(sqrt(m/k)) Thus k= roughly 2
Is this correct? Then I have trouble figuring out the rest because t= T/4 confuses me and I can't find the displacement at this particular time.
You have the wrong equation...
Displacement=20cos wt where
w=2PI *f=2PI/T= 2
displacement= 20 cos 2t
Now calculate displacement as a function of t.