Velocity Displacement Relationship

Q. A body executing linear simple harmonic motion has a velocity of $3cm/s$, when its displacement is $4cm$ and a velocity of $4cm/s$, when its displacement is $3cm$. What is the amplitude of oscillation?

1. $7.5cm$
2. $10cm$
3. $12.5cm$
4. $5cm$

Q.

The maximum speed and acceleration of a particle executing simple harmonic motion are $10cm{s}^{-1}and50cm{s}^{-2}$. Find the position(s) of the particle when the speed is $8c{m}^{-1}$.

1. 

2. 

3. 

4. 

Q. A particle describes linear S.H.M. Its velocities are $3m{s}^{-1}$ and $2m{s}^{-1}$ when its displacements are 2 m and 3 m respectively from mean position. Find length of the path?

1. 6.7 m
2. 7.2 m
3. 1.2 m
4. 4.6 m

Q. Average velocity of a particle executing SHM in one time period is (assuming units to be in S.I.)

1. 0 $m{s}^{-1}$
2. $\frac{A\omega }{2}m{s}^{-1}$
3. $A\omega m{s}^{-1}$
4. $\frac{A{\omega }^2}{2}m{s}^{-1}$

Q. A point performs simple harmonic oscillation of period $T$ and the equation of motion is given by $x=asin(\omega t+\frac{\pi }{6}).$ After the elapse of what fraction of the time peirod, the velocity of the point will be equal to half of its maximum velocity?

1. $\frac{T}{8}$
2. $\frac{T}{6}$
3. $\frac{T}{3}$
4. $\frac{T}{12}$

Q. A particle executes SHM, with an amplitude of $10\text{cm}$. When the particle is at $6\text{cm}$ from the mean position, the magnitude of its velocity is equal to twice of its acceleration. Find the time period (in seconds)

1. $4.1\text{s}$
2. $9.42\text{s}$
3. $14.8\text{s}$
4. $1.17\text{s}$

Q. A particle is executing SHM along a straight line. Its velocities at distances $2\text{cm}$ and $4\text{cm}$ from the mean position are $3\text{cm/s}$ and $2\text{cm/s}$ respectively. Find the time period of SHM.

1. $2\pi \sqrt{\frac{12}{5}}\text{s}$
2. $2\pi \sqrt{\frac{6}{5}}\text{s}$
3. $\pi \sqrt{\frac{8}{5}}\text{s}$
4. $\pi \sqrt{\frac{12}{5}}\text{s}$

Q. A particle performs SHM with a period $T$ and amplitude $A$. The mean velocity of the particle over the time interval during which it travels a distance $\frac{A}{2}$ from the extreme position is

1. $\frac{2A}{T}$
2. $\frac{3A}{T}$
3. $\frac{A}{2T}$
4. $\frac{A}{T}$

Q. The time period of an object performing SHM is $16\text{s}$. It starts its motion from the equilibrium position. After $2\text{s}$ its velocity is $\pi \text{m/s}$. What is its displacement amplitude?

1. $\sqrt{2}\text{m}$
2. $4\sqrt{2}\text{m}$
3. $8\sqrt{2}\text{m}$
4. $2\sqrt{2}\text{m}$

Q. A particle is performing SHM with an amplitude $A$ and angular frequency $\omega$. Find the displacement of the particle from the mean position where the speed of the particle becomes half of the maximum speed.

1. $x=\frac{A}{\sqrt{2}}$
2. $x=\pm \frac{\sqrt{3}A}{2}$
3. $x=\frac{-A}{\sqrt{2}}$
4. $x=\pm \frac{A}{2}$