Forced Oscillations

Q.

What is resonance? Give two examples.

Q. A body of mass $600\text{gm}$ is attached to a spring of spring constant $k=100\text{N/m}$ and it is performing damped oscillations. If damping constant is $0.2$ and driving force is $F=F_0\cos \left(\omega t\right)$ where $F_0=20\text{N}$, find the amplitude of oscillations at resonance.

1. $4.1\text{m}$
2. $0.57\text{m}$
3. $7.75\text{m}$
4. $0.98\text{m}$

Q. Amplitude of vibrations remains constant in case of
$\left(i\right)$ free vibrations
$\left(ii\right)$ damped vibrations
$\left(iii\right)$ maintained vibrations
$\left(iv\right)$ forced vibrations

1. $\left(i\right)$, $\left(iii\right)$ and $\left(iv\right)$
2. $\left(ii\right)$ and $\left(iii\right)$
3. $\left(i\right)$, $\left(ii\right)$ and $\left(iii\right)$
4. $\left(ii\right)$ and $\left(iv\right)$

Q.

A 1000 kg car carrying four 82 kg people travels over a "washboard” dirt road with corrugations 4.0 m apart. The car bounces with maximum amplitude when its speed is 16 km/h. when the car stops, and the people get out, by how much does the car body rise on its suspension?

1. 10 cm

2. 3 cm

3. 5 cm

4. None of these

Q. Amplitude of vibrations remains constant in case of
$\left(i\right)$ free vibrations
$\left(ii\right)$ damped vibrations
$\left(iii\right)$ maintained vibrations
$\left(iv\right)$ forced vibrations

1. $\left(i\right)$, $\left(iii\right)$ and $\left(iv\right)$
2. $\left(ii\right)$ and $\left(iii\right)$
3. $\left(i\right)$, $\left(ii\right)$ and $\left(iii\right)$
4. $\left(ii\right)$ and $\left(iv\right)$

Q. Four pendulums $A,B,C$ and $D$ are suspended from the same elastic support as shown in figure. $A$ and $C$ are of the same length, while $B$ is smaller than $A$ and $D$ is larger than $A$. If $A$ is given a transverse displacement,


[Assume there is no loss of energy]

1. $D$ will vibrate with maximum amplitude
2. $C$ will vibrate with maximum amplitude
3. $B$ will vibrate with maximum amplitude
4. All the four will oscillate with equal amplitude