Oscillations

In Simple Harmonic Motion (SHM), at which position is the velocity of the object at its maximum?

An object's displacement in SHM is described by the equation $x(t) = 0.2 cos(4pi t)$, where $x$ is in meters and $t$ is in seconds. What is the object's velocity at $t = 0$?

In SHM, how is the acceleration related to the displacement?

A mass-spring system has a mass of 2 kg and a spring constant of 200 N/m. What is the period of oscillation?

If the spring constant of a mass-spring system is quadrupled, how does the period change?

A 0.5 kg block is attached to a spring with a spring constant of 50 N/m. The block is stretched 0.1 m from its equilibrium position and released. What is the maximum speed of the block?

A simple pendulum has a length of 1 meter and is on Earth (g ≈ 9.8 m/s²). What is the approximate period of the pendulum's oscillation?

If the length of a simple pendulum is increased by a factor of 9, how will its period change?

A displacement-time graph for an object in SHM shows one complete cycle taking 4 seconds. What is the period of the SHM?

Given a velocity-time graph for SHM, at what point in the cycle does the object have maximum displacement from equilibrium?