A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $\overrightarrow{a}$ is correctly shown in: 

1.		2.
3.		4.

A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure. μ_s is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q will be:

1. kA

2.  $\frac{kA}{2}$

3. Zero

4. μ_s mg

The displacement of a particle along the x-axis is given by $x=a{\sin }^2$ $\omega t$. The motion of the particle corresponds to:

A body performs simple harmonic motion about x=0 with an amplitude a and a time period T. The speed of the body at $\mathrm{x}=\frac{\mathrm{a}}{2}$ will be:
1. $\frac{\mathrm{\pi a}\sqrt{3}}{2\mathrm{T}}$                                         
2. $\frac{\mathrm{\pi a}}{\mathrm{T}}$
3. $\frac{3{\mathrm{\pi }}^2\mathrm{a}}{\mathrm{T}}$                                           
4. $\frac{\mathrm{\pi a}\sqrt{3}}{\mathrm{T}}$

Which one of the following equations of motion represents simple harmonic motion? (where \(k\), \(k_0\), \(k_1\) and  α  are all positive.)
1. Acceleration = -$k_{0}x+k_1{x}^2$\(k_0\)  
2. Acceleration = -$k\left(x+a\right)$
3. Acceleration = k$\left(x+a\right)$
4. Acceleration = kx

Two simple harmonic motions of angular frequency 100 rad s ^-1 and 1000 rad $s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration will be:
1. 1:10
2. 1:10²
3. 1:10³                               
4. 1:10⁴

If the displacement x and the velocity v of a particle executing simple harmonic motion are related through the expression $4v^2=25-x^2$,then its time period will be:

The time period of a spring mass system at the surface of earth is 2 second. What will be the time period of this system on the moon where acceleration due to gravity is $\frac{1}{6}\mathrm{th}$ of the value of g on earth's surface?

A particle is executing SHM with an amplitude \(A\) and the time period \(T\). If at \(t=0\), the particle is at its origin (mean position), then the time instant when it covers a distance equal to \(2.5A\) will be:
1. \( \frac{T}{12} \)
2. \(\frac{5 T}{12} \)
3. \( \frac{7 T}{12} \)
4. \( \frac{2 T}{3}\)

The equations of the displacement of two particles making SHM are represented by y₁ = a sin (ωt + φ) and y₂ = a cos (ωt) respectively. The phase difference of the velocities of the two particles will be:
1. π/2 + φ
2. -φ
3. φ
4. φ - π/2