Velocity Displacement Relationship

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. The particle is executing $\text{SHM}$ on a line $4\text{cm}$ long. If its velocity at mean position is $12\text{cm/s}$, its frequency in $\text{Hertz}$ will be :

1. $\frac{2\pi }{3}$
2. $\frac{3}{2\pi }$
3. $\frac{\pi }{3}$
4. $\frac{3}{\pi }$

Q. A particle executing SHM oscillates between two fixed points separated by $20\text{cm}$. If its maximum velocity is $30\text{cm/s}$, find its velocity when the displacement is $5\text{cm}$ from the mean position.

1. $15\sqrt{3}\text{cm/s}$
2. $20\sqrt{3}\text{cm/s}$
3. $10\sqrt{3}\text{cm/s}$
4. $5\sqrt{3}\text{cm/s}$

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

Q. A particle executes simple harmonic motion on a straight line. The amplitude of oscillation is $2\text{cm}$. At the instant when the displacement of the particle from mean position is $1\text{cm}$, the magnitude of acceleration is equal to the magnitude of velocity. The frequency of the simple harmonic motion is

1. $\frac{\sqrt{3}}{7\pi }\text{Hz}$
2. $\frac{\sqrt{3}}{5\pi }\text{Hz}$
3. $\frac{\sqrt{3}}{2\pi }\text{Hz}$
4. $\frac{\sqrt{3}}{4\pi }\text{Hz}$

Q. The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement ?

1. 
2. 
3. 
4. 

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

Q. The particle is executing $\text{SHM}$ on a line $4\text{cm}$ long. If its velocity at mean position is $12\text{cm/s}$, its frequency in $\text{Hertz}$ will be :

1. $\frac{2\pi }{3}$
2. $\frac{3}{2\pi }$
3. $\frac{\pi }{3}$
4. $\frac{3}{\pi }$

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 of SHM(in seconds)

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

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

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. $\pm 5cm$

2. $\pm 1.2cm$

3. $\pm 3.8cm$

4. $\pm 4.6cm$

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

Q. A particle performing SHM has a velocity $v_0$ at mean position. Find the velocity of the particle, when it reaches a point which is at a distance $\frac{A}{2}$ from the mean position.
[$A=$ amplitude of SHM]

1. $\frac{v_0}{4}$
2. $\frac{\sqrt{3}}{2}{v}_0$
3. $\frac{3v_0}{2}$
4. $\frac{v_0}{\sqrt{2}}$

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 of SHM(in seconds)

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

Q. A particle executing SHM oscillates between two fixed points separated by $20\text{cm}$. If its maximum velocity is $30\text{cm/s}$, find its velocity when the displacement is $5\text{cm}$ from the mean position.

1. $15\sqrt{3}\text{cm/s}$
2. $20\sqrt{3}\text{cm/s}$
3. $10\sqrt{3}\text{cm/s}$
4. $5\sqrt{3}\text{cm/s}$

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