A particle executes linear simple harmonic motion with an amplitude of 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
(a)
(b)
(c)
(d)
A body mass m is attached to the lower end of a spring whose upper end is fixed. The spring has neglible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. The value of m in kg is-
(1)
(2)
(3)
(4)
The damping force on an oscillator is directly proportional to the velocity.The units of the constant of proportionality are
(1)
(2)
(3)
(4)
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. |
The period of oscillation of a mass \(M\) suspended from a spring of negligible mass is \(T.\) If along with it another mass \(M\) is also suspended, the period of oscillation will now be:
1. \(T\)
2. \(T/\sqrt{2}\)
3. \(2T\)
4. \(\sqrt{2} T\)
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
A spring of force constant \(k\) is cut into lengths of ratio \(1:2:3\). They are connected in series and the new force constant is \(k'\). Then they are connected in parallel and force constant is \(k''\). Then \(k':k''\) is:
1. \(1:9\)
2. \(1:11\)
3. \(1:14\)
4. \(1:6\)
A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s2 at a distance of 5 m from the mean position. The time period of oscillation is:
1. | 2 s | 2. | s |
3. | 2 s | 4. | 1 s |
A particle is executing a simple harmonic motion. Its maximum acceleration is and maximum velocity is . Then its time period of vibration will be:
1. | \(\frac {\beta^2}{\alpha^2}\) | 2. | \(\frac {\beta}{\alpha}\) |
3. | \(\frac {\beta^2}{\alpha}\) | 4. | \(\frac {2\pi \beta}{\alpha}\) |