Time Period Independent of Amplitude

Q. A particle is executing SHM along a straight line. Its velocities at distances $x_1$ and $x_2$ from the mean position are $v_1$ and $v_2$ respectively. Its time period of oscillation is

1. $2\pi \sqrt{\frac{x_2^2-x_1^2}{v_1^2-v_2^2}}$
2. $2\pi \sqrt{\frac{v_1^2+v_2^2}{x_1^2+x_2^2}}$
3. $2\pi \sqrt{\frac{v_1^2-v_2^2}{x_1^2-x_2^2}}$
4. $2\pi \sqrt{\frac{x_1^2+x_2^2}{v_1^2+v_2^2}}$

Q.

A particle starts S.H.M. from the mean position. Its amplitude is A and time period is T. At the time when its speed is half of the maximum speed, its displacement y is

[Haryana CEE 1996; CBSE PMT 1996; MH CET 2002]

1. 

2. 

3. 

4. 

Q. An arrow is shot into the air. Its range is 200 metres and its time of flight is 5 sec. If the value of g is assumed to be 10 m/s^2, then the horizontal component of the velocity of arrow is, : (1) 25 m/s (2) 40 m/s (3) 31.25 m/s (4) 12.5 m/s

Q. The maximum speed and acceleration of a particle executing SHM be 20 cm/s and 20cm/s.then its time period is

Q. 62.Time period of spring mass system is T. If this spring is cut into 2 parts whose lenghts are in the ratio 1:3 and the same mass us attached to the longer part thr new time period will be?

Q. A body is projected with speed 55 m/s . Find the distance travelled by it in 6th second of it motion

Q. When a mass m is attached to a spring it oscillates with period 4 s. When an additional mass of 2 kg is attached to a spring, time period increases by 1 s. The value of m is

Q.

In the figure, $S_{1}and{S}_2$ are identical springs. The oscillation frequency of the mass m is f. If one spring is removed, the frequency will become

1. f

2. fx2

3. 

4. 

Q.

A small block oscillates back and forth on a smooth concave surface of radius R. The time period of small oscillation is

1. 

2. 

3. 

4. $2\pi \sqrt{\frac{R}{3g}}$

Q. A PARTICLE IS REVOLVING IN A CIRCLE OF RADIUS R. IF THE FORCE ACTING ON IT IS INVERSELY PROPORTIONAL TO R THEN THE TIME PERIOD IS PROPORTIONAL TO A R B R^2 C 1/R D 1/R^2

Q. if a mass M syspended by a spring executes SHM with time period T and time period becomes 5T/3 if mass is increased by m then find ratio of m/

Q. 1. "Find the time taken by the particle in going from x=0 to x=A/2 where is the amplitude." Why cant we use cosine component instead of sine component.

Q. A body is executing SHM with amplitude a and time period T. The ratio of KE and PE when displacement from the equilibrium position is half the amplitude

Q. the position x of an object as function of time t is x = 2+3t where x is in m and t is in second the acceleration of an object at t = 2s will be

Q. Q, . If a particle performimg S.H.M. with a period of T second, then the time required to reach from midway to extreme position will be?

Q. A body oscillates simple harmonically with an amplitude of 0.05 m. At a certain instant of time its displacement is 0.01 m and acceleration is $1.0m{s}^{-1}$ . What is the period of oscillation?

1. 0.1 s
2. 0.2 s
3. $\frac{\pi }{10}s$
4. $\frac{\pi }{s}s$

Q. 39.n an elevator, a spring clock of time period Ts (mass attached to a spring) and a pendulum clock of time period Tp are kept. If the elevator accelerates upwards. What will happen to the value of Tp and Ts? And why?

Q. 2. A body of mass m is attached to the lower end of a spring whose upper end is fixed the spring has negligible mass when the mass m is slightly pulled Down and released it oscillates with a time period of 3 s when the mass m is increased by 1 kg the time period of oscillations becomes 5 s the value of m in kg is

Q. 42.The time period of mass M when displaced from its equilibrium position and then released for the system as shown in fig is

Q. An air chamber of volume V has a neck area of cross section a into which a ball of mass m just fits and can move up and down without any friction (Fig.14.27). Showthat when the ball is pressed down a little and released , it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal [see Fig. 14.27].

Q. The potential energy of a particle of mass $1\text{kg}$ in motion along the $x-$ axis is given by $U=4(1-\text{cos}2x)\text{J}$, where $x$ is in $\text{m}$. The period of small oscillations (in $\text{s}$) is

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

Q.

A man weighs 70 kg. He stands on a weighing scale in a lift which is moving upwards with an acceleration of 5ms².What would be the reading on the scale? (g=10 ms²).

1. 1050 N

2. 1200 N

3. 220 N

4. 1000 N

Q. A cylindrical conducting piston of mass $M$ slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of a gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be (process is isothermal)

1. $2\pi \sqrt{\frac{Mh}{PA}}$
2. $2\pi \sqrt{\frac{MA}{Ph}}$
3. $2\pi \sqrt{MPhA}$
4. $2\pi \sqrt{\frac{M}{PAh}}$

Q. 53.A pendulum inside on elevator has time period T1 when the elevator is at rest , T2 when the elevator us accelerated up with a uniform acceleration a and T3 when the elevator accelerated down with same acceleration then the relation between the time periods is

Q. Particle performing SHM with amplitude A. Its speed is tripled at the ins†an t when it is at a dis†an ce 2A/3 from equilibrium position.New amplitude =

Q. The maximum velocity and acceleration of a particle in $\text{SHM}$ are $100\text{cm/s}$ and $157{\text{cm/s}}^2$ respectively. The time period in seconds will be :

1. $4$
2. $1.57$
3. $0.25$
4. $1$

Q. A cylindrical block of density $d$ stays fully immersed in a beaker filled with two immiscible liquids of different densities $d_1$ and $d_2$. The block is in equilibrium with half of it in liquid $1$ and the other half in liquid $2$ as shown in the figure. If the block is given a displacement downwards and released, then neglecting friction, which of the following statement(s) is/are correct?

1. Block executes simple harmonic motion.
2. The block's motion is periodic but not simple harmonic.
3. The frequency of oscillation is independent of the size of the block.
4. The motion of the block is symmetric about its equilibrium position.

Q. a particle passes a given point moving downward with a velocity of 50m/s.how long before this was it moving upward at the same rat

Q. A particle exhibits linear simple harmonic motion with an amplitude of $3cm$. When the particle is at $2cm$ from the mean position, the magnitude of its velocity is equal to that of its acceleration. Its time period in seconds is

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

Q. A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of $40\text{cm}$. The block just loses contact with the plank when the later is at momentary rest. Then:

1. The period of oscillation is $\left(\frac{2\pi }{5}\right)$
2. The block weighs double its weight, when the plank is at one of the positions of momentary rest.
3. The block weights 0.5 times its weight on the plank halfway up
4. The block weights 1.5 times its weight on the plank halfway down