Oscillations

Which of the following equations represents the displacement of an object in Simple Harmonic Motion (SHM)?

An object's displacement in SHM is given by $x = 4sin(2t)$, where $x$ is in meters and $t$ is in seconds. What is the object's displacement at $t = frac{pi}{4}$ seconds?

The motion of a block attached to a spring is described by the differential equation $\frac{d^2x}{dt^2} = -25x$. If the mass of the block is 2 kg, what is the spring constant?

A mass oscillating on a spring has an amplitude of 0.1 m and an angular frequency of 10 rad/s. What is the maximum velocity of the mass?

What happens to the amplitude of oscillation when a system is driven at its resonance frequency?

A swing has a natural frequency of 0.5 Hz. If you push the swing at a frequency of 0.5 Hz, what will happen to the swing's motion?

In Simple Harmonic Motion, what is the relationship between acceleration and displacement?

A particle undergoes SHM with an amplitude A and angular frequency $\omega$. If the initial position is $x = frac{A}{2}$ at $t = 0$, and the particle is moving towards the equilibrium position, what is the phase constant $\phi$?

What phenomenon occurs when an external force is applied to an oscillating system at its natural frequency?

Which of the following differential equations describes Simple Harmonic Motion (SHM)?