Damped Oscillations

Q.

For the damped oscillator shown, the mass m of the block is 200 g, k = 90 N m${}^{-1}$ and the damping constant b is 40 g s${}^{-1}$. What is the period of oscillation, time taken for its amplitude of vibrations to drop to half of its initial value.

1. 1s, 6.93s

2. 0.3s, 6.93s

3. 0.6s, 6.93s

4. 0.3s, 3s

Q.

For the damped oscillator system shown with m = 250g, k = 85 N/m, and b = 70 g/s, what is the ratio of the oscillation amplitude at the end of 20 cycles to the initial oscillation amplitude?

1. 1:2

2. 19:50

3. 20:21

4. 5:6

Q.

You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system, the suspension hangs 15 cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by $50\%$ during one complete oscillation. The values of the spring constant k and the damping constant b for the spring and shock absorber system of one wheel (assuming that each wheel supports 750 kg) are:

1. 2 × 10⁵ Nm^-1, 1.8 kg s^-1

2. 5 × 10⁴ Nm^-1, 8.1 kg s^-1

3. 2 × 10⁵ Nm^-1, 1344 kg s^-1

4. 5 × 10⁴ Nm^-1, 1344 kg s^-1

Q. Shock absorbers in automobiles is an application of damped oscillation.

1. True
2. False

Q. The magnitude of damping will when the body of the spring-mass system is immersed in water.

1. increase
2. decrease
3. remains same

Q. In case of damped oscillation the frequency of oscillation is

1. greater than natural frequency
2. less than natural frequency
3. equal to natural frequency
4. both $\left(a\right)$ and $\left(b\right)$

Q. In damped oscillations, if the amplitude becomes half of its maximum value in $1\text{s}$, then after $2\text{s}$ amplitude will be
($A_o$ is initial amplitude)

1. $\frac{A_o}{4}$
2. $\frac{A_o}{2}$
3. $A_o$
4. $\frac{\sqrt{3}{A}_o}{2}$

Q. The amplitude of a damped oscillation becomes half in $1\text{minute}$. If the amplitude after $4\text{minute}$ will be $\frac{1}{y}$ times of the original, find the value of $y$.

1. $4$
2. $8$
3. $16$
4. $32$

Q. A weakly damped harmonic oscillator of frequency $n_1$ is driven by an external periodic force of frequency $n_2$. When the steady state is reached, the frequency of the oscillator will be

1. $n_1$
2. $n_2$
3. $\frac{n_1+n_2}{2}$
4. $(n_1+n_2)$

Q. In the case of sustained forced oscillations the amplitude of oscillations,

1. Decreases sinusoidally
2. Decreases exponentially
3. Always remains constant
4. Decreases linearly