Frequency to Angular Frequency

Q. A spring mass system hanging from the ceiling of an elevator is at rest. The elevator starts accelerating upwards with acceleration 'a'. 'm' is the mass of block and 'k' is the spring constant of spring. Then choose the correct alternative(s).

1. Amplitude of oscillation is $\frac{ma}{k}$
2. Amplitude of oscillation is $\frac{mg}{k}$
3. Time period of oscillation is $2\pi \sqrt{\frac{m}{k}}$
4. Time period of oscillation is $2\pi \sqrt{\frac{2m}{k}}$

Q. Two identical strings of a stringed musical instrument are in unison when stretched with the same tension. When the tension in one string is increased by $1\%$, the musician hears 4 beats per second. What was the frequency of the note when the strings were in unison?

1. 796 Hz
2. 800 Hz
3. 804 Hz
4. 808 Hz

Q. What is the relation between frequency f of and oscillation and its angular frequency $\omega$

1. $\omega$ = 2 $\pi$f
2. 2 $\pi \omega$ = f

Q. Two identical strings of a stringed musical instrument are in unison when stretched with the same tension. When the tension in one string is increased by $1\%$, the musician hears 4 beats per second. What was the frequency of the note when the strings were in unison?

1. 796 Hz
2. 800 Hz
3. 804 Hz
4. 808 Hz

Q. Angular frequency is defined as the rate of change of angular displacement.

1. True
2. False

Q.

1. 

2. 

3. 

4. 

Q. A $1\text{kg}$ block is executing simple harmonic motion of amplitude $0.1\text{m}$ on a smooth horizontal surface under the restoring force of a spring of spring constant $100\text{N/m}$. A block of mass $3\text{kg}$ is gently placed on it at the instant it passes through the mean position. Assuming that the blocks move together, then

1. Amplitude of the motion becomes $5\text{cm}$
2. The oscillation frequency becomes $\frac{5}{2\pi }\text{Hz}$
3. Amplitude of the motion becomes $10\text{cm}$
4. The oscillation frequency becomes $\frac{5}{\pi }\text{Hz}$