$y={\sin }^3\omega t is$:

1.	a simple harmonic function.
2.	a simple harmonic function but not a periodic function.
3.	both periodic and simple harmonic function.
4.	only periodic function.

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. (Take the direction from A to B as the positive direction.) The signs of velocity, acceleration, and force on the particle when it is at 3 cm away from A going towards B are:

1. Zero, Negative, Negative

2. Negative, Zero, Zero

3. Negative, Negative, Negative

4. Positive, Positive, Positive

Which of the following relationships between the acceleration '\(a\)' and the displacement '\(x\)' of a particle involves simple harmonic motion?

A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?

1. 219 N

2. 196 N

3. 223 N

4. 225 N

A spring having a spring constant of 1200 N/m is mounted on a horizontal table as shown in the figure. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. The frequency of oscillations will be:
    

A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The maximum acceleration of the mass is:

        
1. \(6\) ms^-2
2.  \(8\) ms^-2
3.  \(3.3\) ms^-2
4.  \(5.1\) ms^-2

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?

1. 50 m/min
2. 150 m/min
3. 100 m/min
4. 120 m/min

The acceleration due to gravity on the surface of the moon is 1.7 m $s^{-2}$. What is the time period of a simple pendulum on the surface of the moon if its time period on the surface of the earth is 3.5 s? (g on the surface of the earth is 9.8 m $s^{-2}$ )

1. 7.3 s
2. 6.4 s
3. 5.5 s
4. 8.4 s

What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?
1. \(100\) s^-1 
2. zero
3.  \(150\) s^-1
4. none of these 

A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?
1. \(\mathrm{T}=2 \pi \sqrt{\frac{1}{\sqrt{\mathrm{g}^2+\frac{\mathrm{v}^4}{\mathrm{R}^2}}}}\)
2. \(\mathrm{T}=4 \pi \sqrt{\frac{\mathrm{l}}{\mathrm{g}^2+\frac{\mathrm{v}^4}{\mathrm{R}^2}}}\)
3. \(\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{l}}{\mathrm{g}^2+\frac{\mathrm{v}^3}{\mathrm{R}^2}}}\)
4. \(\mathrm{T}=4 \pi \sqrt{\frac{1}{\sqrt{\mathrm{g}^2+\frac{\mathrm{v}^4}{\mathrm{R}^4}}}}\)