Question

A mass of 2.9 kg is connected to a horizontal spring whose stiffness is 9 N/m. When the spring is relaxed, x = 0. The spring is stretched so that the initial value of x = +0.14 m. The mass is released from rest at time t = 0. Remember that when the argument of a trigonometric function is in radians, on a calculator you have to switch the calculator to radians or convert the radians to degrees.

Predict the position x when t = 1.43 s:

Answer 1

F = ma gives
-T = ma where T = kx = 9x

-9x = 2.9a where a = accn = vdv/dx or d^2x/dt^2

d^2x/dt^2 = -90x/29

compare this with d^2x/dt^2 = - w^2x which has solution x = Acoswt + Bsinwt or Csin(wt + K1) or Dcos(wt + K2)

You choose which solution - it doesn't matter.

x = Acoswt + Bsinwt
When t = 0, x = 0.14 so 0.14 = A

x = 0.14coswt + Bsinwt

When t = 0 then dx/dt = 0

dx/dt = -0.14wsinwt +Bwcoswt so that

0 = Bw which means B = 0 and so the solution is

x = 0.14coswt remember that w^2 = 90/29

When t = 1.43 then we have

x = 0.14cos1.43w

x ~ 0.14 m