KE & PE Graph

Q.

$Y=A\sin (\omega t+{\varphi }_0)$is the time – displacement equation of an SHM, At t = 0, the displacement of the particle is $Y=\frac{A}{2}$and it is moving along negative x-direction. Then, the initial phase angle ${\varphi }_0$will be.

1. $\frac{\mathrm{\pi }}{6}$

2. $\frac{\mathrm{\pi }}{3}$

3. $\frac{2\mathrm{\pi }}{3}$

4. $\frac{5\mathrm{\pi }}{6}$

Q. The displacement time graph of a particle executing S.H.M. is given in figure : (sketch is schematic and not to scale)

Which of the following statements is/are true for this motion?
$\left(a\right)$The force is zero at $t=\frac{3T}{4}$
$\left(b\right)$The acceleration is maximum at $t=T$
$\left(c\right)$The speed is maximum at $t=\frac{T}{4}$
$\left(d\right)$The P.E. is equal to K.E. of the oscillation at $t=\frac{T}{2}$

1. $\left(a\right),\left(b\right)$ and $\left(d\right)$
2. $\left(b\right),\left(c\right)$ and $\left(d\right)$
3. $\left(a\right),\left(b\right)$ and $\left(c\right)$
4. $\left(a\right)$ and $\left(d\right)$

Q. Two simple harmonic motion, are represented by the equations $y_1=10\sin (3\pi t+\frac{\pi }{3})$

$y_2=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)$
Ratio of amplitude of

$y_1$ to $y_2=x:1.$
The value of $x$ is _________.

Q. For a particle executing S.H.M. the displacement $x$ is given by $x=A\cos \omega t$. Identify the graph which represents the variation of potential energy $\text{(P.E.)}$ as a function of time $t$ and displacement $x$.

1. $\text{II, IV}$
2. $\text{II, III}$
3. $\text{I, III}$
4. $\text{I, IV}$

Q. A particle of mass m is placed in one-dimensional potential field where potential energy varies as $U\left(x\right)=U_0$ $(1-\cos bx)$ where $U_0$ and b are constants. The period of small amplitude oscillation of the particle is

1. 
2. 
3. 
4. 

Q. The ratio of maximum and minimum intensities of two sources is $4:1.$ The ratio of their amplitudes is-

1. $1:3$
2. $3:1$
3. $1:9$
4. $1:1$

Q. A body executes simple harmonic motion. The potential energy $\left(PE\right)$, the kinetic energy $\left(KE\right)$ and total energy $\left(TE\right)$ are measured as a function of displacement $\left(x\right)$. Which of the following statements is true?

1. $PE$ is maximum when $x=0$
2. $KE$ is maximum when $x=0$
3. $TE$ is zero when $x=0$
4. $KE$ is maximum when $x$ is maximum

Q. A simple harmonic motion is given by the equation
$x=3sin3\pi t+4cos3\pi t$
where x is in metres. The amplitude of the motion is

1. 3 m
2. 4 m
3. 5 m
4. 7 m

Q. The period of a particle in SHM is $8\text{s}$. At $t=0$, it is at the mean position. The ratio of the distance travelled by it in the $1^{\text{st}}$ and the $2^{\text{nd}}$ second is

1. $\frac{1}{2}$
2. $\frac{1}{\sqrt{2}}$
3. $\sqrt{2}$
4. $\sqrt{2}+1$

Q.

If one joule of energy is converted to a new system of units in which length is measured in 10m, mass in 10 kilogram and time in 1 minute.What is the value of energy in this new system.

Q.

What is the maximum extension in the spring shown in figure?

1. None

2. 

3. 

4. 

Q.

For a S.H.M., amplitude is 6 cm. If instantaneous potential energy is half the total energy then distance of particle from its mean position is

1. 3 cm

2. 4.2 cm

3. 5.8 cm

4. 6 cm

Q.

Please help me to convert 1kWh into J using dimensional analysis.

Q.

A particle executes S.H.M of amplitude a

1. At what distance from mean position is it's K.E is equal to its P.E

2.At what point is its speed half the maximum speed

Q.

Graph shows the x(t) curves for three experiments involving a particular spring-block system oscillating in SHM. The kinetic energy of the system is maximum at t=4 sec, for the situation:

1. 1

2. 2

3. 3

4. same in all

Q. $x_1=A\sin (\omega t-0.1x)$ and $x_2=A\sin (\omega t-0.1x-\frac{\varphi }{2})$. Resultant amplitude of combined wave is

1. $2A\cos \frac{\varphi }{4}$
2. $A\sqrt{2\cos \varphi /2}$
3. $2A\cos \frac{\varphi }{2}$
4. $A\sqrt{2(1+\cos \frac{\varphi }{4})}$

Q. A body is in motion along the positive $x$ - axis, according to the relation $x=a{\sin }^2\omega t$. Then, the variation of its kinetic energy $K$ with time $t$ may be represented by

1. 
2. 
3. 
4. 

Q. The three particles, each having mass $m$, is kept at corners of an equilateral triangle of side length $a$ and are rotating under the effect of mutual gravitational force. Choose the correct alternative(s).

1. The radius of circular path followed by the particles is $\frac{a}{2}$.
2. Velocity of the particles is $\sqrt{\frac{Gm}{a}}$.
3. Binding energy of the system is $\frac{1.5G{m}^2}{a}$.
4. Time period of the particles is $\sqrt{\frac{\pi a^2}{2Gm}}$.

Q. A particle executes simple harmonic motion with a frequency f. The frequency with which its kinetic energy oscillates is

1. f
2. 2f
3. 4f
4. f/2

Q. Graph shows the $x\left(t\right)$ curves for three experiments involving a particular spring - block system executing SHM.
Which of the following situations shown in the graph, has the highest value of maximum kinetic energy of the system at $t=4\text{sec}$.

1. $1$
2. $2$
3. $3$
4. Same in all

Q. A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency $1\text{Hz}$. If the bottom half of the stick is cut off, then its new frequency for small oscillation (in $\text{Hz}$) would become

Q.

What is the work to be done to increase the velocity of a car from $30km{h}^{-1}to60km{h}^{-1}$ if the mass of car is $1500kg$?

Q. Graph shows the $x\left(t\right)$ curves for three experiments involving a particular spring - block system executing SHM.
Which of the following situations shown in the graph, has the highest value of maximum kinetic energy of the system at $t=4\text{sec}$.

1. $2$
2. $3$
3. Same in all
4. $1$

Q. The potential energy of a particle oscillating on x-axis is $U=20+(x-2{)}^2$. Here U is in joules and x in meters. Total mechanical energy of the particle is 36 J.
a)State whether the motion of the particle is simple harmonic or not.
b)Find the mean position.
c)Find the maximum kinetic energy of the particle.

Q. The displacement of a particle executing simple harmonic motion is given by
$x\left(t\right)=2\sin \left(2\pi t\right)+2\cos (2\pi t+\frac{\pi }{6})$
The total energy of the particle is $(m=1\text{kg}$)

1. $2{\pi }^2\text{J}$
2. $8{\pi }^2\text{J}$
3. $6{\pi }^2\text{J}$
4. $3{\pi }^2\text{J}$

Q.

A particle free to move along the x-axis has potential energy given by $U\left(x\right)=k(1-e^{-x^2})$ For $-\infty <x<\infty$, where k is a positive constant of appropriate dimensions. Then

1. If its total mechanical energy is U, it has its minimum kinetic energy at the origin

2. For small displacements from x = 0, the motion is simple harmonic

3. For any finite non-zero value of x, there is a force directed away from the origin

4. At points away from the origin, the particle is in unstable equilibrium

Q.

Two bodies which are equal in mass, move with uniform velocities of $6m{s}^{-1}$ and $18m{s}^{-1}$, respectively. Find the ratio of their kinetic energies.

Q. The displacement - time relation for a particle can be expressed as $y=0.5\left[{\cos }^2\right(n\pi t)-{\sin }^2(n\pi t\left)\right]$. This relation shows that

1. the particle is executing SHM with amplitude $0.5\text{m}$
2. the particle is executing SHM with a frequency $n$ times that of a second's pendulum
3. the particle is executing SHM and the velocity at its mean position is $\left(n\pi \right)\text{m/s}$
   
4. the particle is not executing SHM at all

Q. A particle executes simple harmonic motion with frequency $f_1$, the frequency with which kinetic energy oscillates is $f_2$, the frequency with which potential energy oscillates is $f_3$, then $f_1:f_2:f_3$ is

1. 1 : 2 : 2
2. 1 : 2 : 4
3. 1 : 2 : 1
4. 1 : 1 : 2

Q. Graph shows the $x\left(t\right)$ curves for three experiments involving a particular spring - block system executing SHM.
Which of the following situations shown in the graph, has the highest value of maximum kinetic energy of the system at $t=4\text{sec}$.

1. $1$
2. $2$
3. $3$
4. Same in all