The vibration of a component in a machine is represented by the equation: $x=3.0\times {10}^{-4}\sin \left(240\pi t\right)$. Where, the displacement $x$ is in metres. Determine the: Amplitude

The vibration of a component in a machine is represented by the equation: 

$x=3.0\times {10}^{-4}\sin \left(240\pi t\right)$. 

Where, the displacement $x$ is in metres. Determine the frequency

The vibration of a component in a machine is represented by the equation:

 $x=3.0\times {10}^{-4}\sin \left(240\pi t\right)$. 

Where, the displacement $x$ is in metres. Determine the $c$ Period of the vibration.

A trolley is at rest, tethered between two springs. It is pulled $0.15 \mathrm{m}$ to one side and, when time $t=0$, it is released so that it oscillates back and forth with S.H.M. The period of its motion is $2.0 \mathrm{s}$. Write an equation for its displacement $x$ at any time $t$ (assume that the motion is not damped by frictional forces).

A trolley is at rest, tethered between two springs. It is pulled $0.15 \mathrm{m}$ to one side and, when time $t=0$, it is released so that it oscillates back and forth with s.h.m. The period of its motion is $2.0 \mathrm{s}$.

Sketch a displacement-time graph to show two cycles of the motion, giving values where appropriate.

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.

A short pendulum oscillates with s.h.m. such that its acceleration $a$ (in ${\mathrm{ms}}^{-2}$ ) is related to its displacement $x$ (in $\mathrm{m}$ ) by the equation $a=-300x$.

Determine the frequency of the oscillations.

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.