Answer to Question #314048 in Mechanics | Relativity for Mae

Question

the elastic constant of a helical spring is 9 N/m. a 1 kg body is attached from the spring and is made to move with simple harmonic motion. determine the period of vibration of the body and the acceleration when the body is 40 cm from its equilibrium position if the amplitude is 80 cm

Answer 1

$\omega=\sqrt\frac km=3~\frac{rad}s,$

$T=\frac{2\pi}{\omega}=2.1~s,$

$x=0.8\cos 3t,$

$0.4=0.8\cos 3t,$

$t=\frac \pi 9=0.35~s,$

$v=-2.4\sin 3t,$

$a=-7.2\cos 3t,$

$a(\frac \pi 9)=-3.6~\frac m{s^2}.$