A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector 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. μs 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.
3. Zero
4. μs mg
A simple pendulum has a time period when on the earth’s surface, and when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of is:
1. 1
2.
3. 4
4. 2
The displacement of a particle along the x-axis is given by . The motion of the particle corresponds to:
1. | simple harmonic motion of frequency ω / π. |
2. | simple harmonic motion of frequency 3 ω / 2 π. |
3. | non-simple harmonic motion. |
4. | simple harmonic motion of frequency ω / 2 π. |
A body performs simple harmonic motion about x=0 with an amplitude a and a time period T. The speed of the body at will be:
1.
2.
3.
4.
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 = -\(k_0\)
2. Acceleration = -
3. Acceleration = k
4. Acceleration = kx
Two simple harmonic motions of angular frequency 100 rad s -1 and 1000 rad 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 ,then its time period will be:
1. | \(\pi \) | 2. | \(2 \pi \) |
3. | \(4 \pi \) | 4. | \(6 \pi\) |
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 of the value of g on earth's surface?
1. | \(\frac{1}{\sqrt{6}} ~\mathrm{seconds} \) | 2. | \(2 \sqrt{6}~ \mathrm{seconds} \) |
3. | \(2~ \mathrm{seconds} \) | 4. | \( 12~\mathrm{ seconds}\) |
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. | \( \dfrac{T}{12} \) | 2. | \(\dfrac{5 T}{12} \) |
3. | \( \dfrac{7 T}{12} \) | 4. | \(\dfrac{2 T}{3}\) |