A simple pendulum performs simple harmonic motion about $x = 0$ with an amplitude $a$ and time period $T$. The speed of the pendulum at $x = \frac{a}{2}$ will be:

The restoring force of a spring, with a block attached to the free end of the spring, is represented by:

The displacement-time ($x-t$) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2$ s is:

A particle executing simple harmonic motion has a kinetic energy of $K = K_0 \cos^2(\omega t)$. The values of the maximum potential energy and the total energy are, respectively:

When two displacements represented by $y_1 = a \sin(\omega t)$ and $y_2 = b \cos(\omega t)$ are superimposed, the motion is:

From the given functions, identify the function which represents a periodic motion:

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then, its time period in seconds is:

Match List-I with List-II. **List-I (Graphs)** (a) Displacement-time graph with decreasing amplitude (Damped) (b) Displacement-time graph with constant amplitude (Undamped) (c) Force-displacement graph (Linear relationship, F = -kx) (d) Energy-time graph (Constant total energy) **List-II (Situations)** (i) Total mechanical energy is conserved (ii) Bob of a pendulum is oscillating under negligible air friction (iii) Restoring force of a spring (iv) Bob of a pendulum is oscillating along with air friction Choose the correct answer from the options given below:

The oscillation of a body on a smooth horizontal surface is represented by the equation, $X = A \cos(\omega t)$, where $X =$ displacement at time $t$, $\omega =$ frequency of oscillation. Which one of the following graphs correctly shows the variation of acceleration, $a$ with time, $t$? ($T =$ time period)