SHM Formulae

Q.

A particle is moving on x-axis has potential energy $U=2-20x+5x^2$ J along x-axis. The particle is released at x=-3. The maximum value of x will be [x is in meter and U is in joule]

1. 5 m

2. 3 m

3. 7 m

4. 8 m

Q. The potential energy of a particle oscillating along $X-$ axis is given as $U=15+4x+(2x-3{)}^2$, where $U$ is in Joules and $x$ in metres. Total mechanical energy of the particle is $36\text{J}$. Mass of particle is $2\text{kg}$. Then,

1. Angular frequency of SHM will be $2\text{rad/sec}$
2. Kinetic Energy at mean position $=16\text{J}$
3. Amplitude of SHM is $2\text{m}$
4. None of these

Q.

A particle of mass 40 g executes a simple harmonic motion of amplitude 2.0 cm. If the time period is 0.20 s, find the total mechanical energy of the system.

1. 7.9J

2. 3.5 $\times$ 10${}^{-3}$J

3. 7.9$\times$ 10${}^{-3}$J

4. 35J

Q. Two simple harmonic motions $y_1=A\sin \omega t$ and $y_2=A\cos \omega t$ are superimposed on a particle of mass $m$. The total mechanical energy of the particle is :

1. $\frac{1}{2}m{\omega }^2{A}^2$
2. $m{\omega }^2{A}^2$
3. $\frac{1}{4}m{\omega }^2{A}^2$
4. zero

Q.

Two blocks A and B each of mass m are connected by a massless spring of natural length L and spring constant K. The blocks are initially resting on a smooth horizontal floor with spring at its natural length as shown in the figure. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B and collides with A. Then,

1. The KE of the A-B system at maximum compression of the spring is zero

2. The KE of the AB system at maximum compression of the spring is $\frac{m{v}^2}{2}$

3. The maximum compression of the spring is $v\sqrt{\frac{m}{k}}$

4. The maximum compression of the spring is $v\sqrt{\frac{m}{2k}}$

Q.

A particle is moving on x-axis has potential energy $U=2-20x+5x^2$ J along x-axis. The particle is released at x=-3. The maximum value of x will be [x is in meter and U is in joule]

1. 5 m

2. 3 m

3. 7 m

4. 8 m

Q. As shown in figure, two light springs of force constant $300\text{N/m}$ and $600\text{N/m}$ oscillate a block of mass $10\text{kg}$. Find the effective force constant.

1. $150\text{N/m}$
2. $200\text{N/m}$
3. $300\text{N/m}$
4. $600\text{N/m}$