A force of 400 Newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. After finding the equation of motion, calculate x(t = pi/12).

I know this is a second order differential equation but I don't know where to start.
k=245.25
w(frequency)=2.2147 hz

The general formula is x(t)=c1cos(wt) +c2sin(wt)
and I think x(0)=10 but help would be really appreciated.

Question

A force of 400 Newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. After finding the equation of motion, calculate x(t = pi/12).

I know this is a second order differential equation but  I don't know where to start.
k=245.25
w(frequency)=2.2147 hz

The general formula is x(t)=c1cos(wt) +c2sin(wt)
and I think x(0)=10 but help would be really appreciated.

barrycarter · Answer

I think you mean x'(0) = 10 since the initial speed is 10, not the initial position?