Question

A 23.3-kg mass is attached to one end of a horizontal spring, with the other end of the spring fixed to a wall. The mass is pulled away from the equilibrium position (x = 0) and released. It then oscillates in simple harmonic motion with a frequency of 4.91 Hz. If the mass’s maximum acceleration during the motion is 135 m/s2, how far from equilibrium was the mass initially pulled?

Answer 1

As we know that angular frequency of SHM is given as

$\omega = 2\pi f$

f = 4.91 Hz

$\omega = 2\pi (4.91)$

$\omega = 30.85 rad/s$

now we know that maximum acceleration during SHM is given by

$a_{max} = \omega^2 A$

$a_{max} = 30.85^2 A$

$135 m/s^2 = 951.75(A)$

now we will have

$A = 0.142 m$

so its maximum displacement will be 14.2 cm