Simple Harmonic Motion Questions

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2\times 10^{-2}\cos \pi t$ metres. The time at which the maximum speed first occurs is:

A point mass oscillates along the $x$ -axis according to the law $x=x_0\cos (\omega t-\pi /4)$. If the acceleration of the particle is written as $a=A\cos (\omega t+\delta )$, then:

Two springs, of force constants $k_1$ and $k_2$, are connected to a mass $m$ as shown (in parallel configuration). The frequency of oscillation of the mass is $f$. If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes:

A particle of mass $m$ executes simple harmonic motion with amplitude $a$ and frequency $\nu$. The average kinetic energy during its motion from the position of equilibrium to the end (one-quarter cycle) is:

The function ${\sin }^2(\omega t)$ represents:

Two simple harmonic motions are represented by the equation $y_1=0.1\sin (100\pi t+\pi /3)$ and $y_2=0.1\cos \pi t$. The phase difference of the velocity of particle $1$ w.r.t. the velocity of the particle $2$ is:

If a simple harmonic motion is represented by $\frac{d^{2}x}{d{t}^2}+\alpha x=0$, its time period is:

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would: