A mass secured at the end of a spring moves with s.h.m. The frequency of its motion is $1.4 \mathrm{Hz}$. Write an equation of the form $a=-{\omega }^{2}x$ to show how the acceleration of the mass depends on its displacement.

A mass secured at the end of a spring moves with s.h.m. The frequency of its motion is $1.4 \mathrm{Hz}$. Calculate the acceleration of the mass when it is displaced $0.050 \mathrm{m}$ from its equilibrium position.

The pendulum of a grandfather clock swings from one side to the other in $1.00 \mathrm{s}$. The amplitude of the oscillation is $12 \mathrm{cm}$. Calculate the period of its motion.

The pendulum of a grandfather clock swings from one side to the other in $1.00 \mathrm{s}$. The amplitude of the oscillation is $12 \mathrm{cm}$. Calculate the frequency.

The pendulum of a grandfather clock swings from one side to the other in $1.00 \mathrm{s}$. The amplitude of the oscillation is $12 \mathrm{cm}$. Calculate the angular frequency.

The pendulum of a grandfather clock swings from one side to the other in $1.00 \mathrm{s}$. The amplitude of the oscillation is $12 \mathrm{cm}$.

Write an equation of the form to show how the acceleration of the pendulum bob depends on its displacement.

The pendulum of a grandfather clock swings from one side to the other in $1.00 \mathrm{s}$. The amplitude of the oscillation is $12 \mathrm{cm}$. Calculate the maximum speed of the pendulum bob.

The pendulum of a grandfather clock swings from one side to the other in $1.00 \mathrm{s}$. The amplitude of the oscillation is $12 \mathrm{cm}$. Calculate the speed of the bob when its displacement is $6 cm.$

A trolley of mass $m$ Is fixed to the end of a spring. The spring can be compressed and extended. The spring has a force constant $k$. The other end of the spring is attached to a vertical wall. The trolley lies on a smooth horizontal table. The trolley oscillates when it is displaced from its equilibrium position. Show that the motion of the oscillating trolley is S.H.M.