Spring Block System: Period & Max Speeds/Accel

[UrbanXrisis]

a 1 kg mass attached to a spring with a force constant of 25 oscillates on a horizontal, frictionless track. At time t=0, the mass is released from rest at x=-3cm (the spring is compressed by 3cm). Find (a) the period of its motion. b) the max values of speed and acceleration. c) the displacement, velocity, acceleration as a function of time.

a)
$$T=2\pi \sqrt{\frac{m}{k}}$$
$$T=2\pi \sqrt{\frac{1kg}{25N/m}}$$
$$T=1.257s$$

b)
$$v_{max}=\omega A=\sqrt{\frac{k}{m}}*A =\sqrt{\frac{25}{1}}*0.03=0.15m/s$$
$$a_{max}=\omega ^2 A=\frac{kA}{m} ={\frac{25}{1}}*0.03=0.75m/s^2$$

c)
$$x=-0.03cos25t$$
$$v=0.15sin25t$$
$$a=0.75cos25t$$

is this all correct?

 

[quasar987]

Looking sexy.

 

[UrbanXrisis]

so the period does not involve how much was pulled back?

 

[quasar987]

Nah.

And this is understandable since if you pull the block back a lot, sure it has a "longer way to go" to the equilibrium position, but it has more energy at its disposal.