(a) In Example 15.3 is the initial condition that \(v_{x}=0\) satisfied by Eq. 15.7?

(b) Is it correct to say that the \(x\) component of the velocity given by Eq. 15.7 must be positive whenever \(x\) is negative so as to make sure that the cart moves back to its equilibrium position?

Data from Example 15.3

A cart of mass \(m=0.50 \mathrm{~kg}\) fastened to a spring of spring constant \(k=14 \mathrm{~N} / \mathrm{m}\) is pulled \(30 \mathrm{~mm}\) away from its equilibrium position and then released with zero initial velocity. What are the cart's position and the \(x\) component of velocity \(2.0 \mathrm{~s}\) after being released?

Vx = dx dt = wA cos(wt) (simple harmonic motion) (15.7)