Spring Block's Time Period

Q. Two masses m1 and m2 are suspended together by a massless spring of spring constant k. When the masses are in equilibrium m1, is removed without disturbing the system, then the angular frequencyand amplitude of oscillations of m2 are

Q. a rod of mass m and length is hinged to its one end and held vertical . a point mass m is attached to other end is allowed to rotate about the hinge .the velocity of rod when it becomes horizontal is

Q. Imagine a narrow tunnel between the two diametrically opposite points of the earth. A particle of mass m is released in this tunnel. The time period of oscillation i

Q. 82. Consider a system of two identical particles.one of the particle is at rest ant the other has an acceleration f. The centre of mass has an acceleration 1. Zero 2. f 3.f/2 4.2f

Q. a particle is executing simple harmonic motion .its max acceleration is alpha and max velocity is beta then its time period of vibration willl be

Q. Two light springs of force constant $K_1$ and $K_2$ and a block of mass $m$ are arranged in one line $AB$ on a smooth horizontal table such that one end of each spring is fixed on rigid supports and the other end is free as shown in the figure. The distance $CD$ between the free ends of the spring is $60\text{cm}$. If the block moves along $AB$ with a velocity $120\text{cm/s}$ in between the springs, calculate the period of oscillation of the block.
(Assume that the dimensions of the cube is much less than $60\text{cm}$)
$(K_1=1.8\text{N/m},K_2=3.2\text{N/m},m=200\text{gm})$

1. $1.41\text{s}$
2. $2.83\text{s}$
3. $5.64\text{s}$
4. $1.92\text{s}$

Q.

A mass m = 2.0 kg is attached to a spring having a force constant k = 290 N/m as in the figure. The mass is displaced from its equilibrium position and released. Its frequency of oscillation (in Hz) is approximately:

1. 1.9

2. 0.50

3. 0.01

4. 12

Q.

A particle moving along the x-axis executes simple harmonic motion, then the force acting on it is given by

[CBSE PMT 1994]

1. - A Kx

2. A cos (Kx)

3. A Kx

4. A exp (- Kx)

Q. Find elongation in spring if one end of spring is attached to rigid point and other point to block of mass m if 1. block is released slowly 2. block is suddenly released and also find acceleration of block at x=0 and at maximum elongatio

Q. A wheel and an axle is made to rotate about a horizontal axis with the help of a body of mass 5 kg attached to a string wound around the axle. The radius of the axle is 10 cm. The body falls vertically throught 5 m is 10 s starting from rest. The moment of inertial of the wheel and axle is (1)3.85 kg m2 (2) 4.85 kg m2 (3) 5.85 kg m2 (4) 2.85 kg m2

Q. In an experiment , sonometer wire vibrates in 4 loops when a 50g weight is placed in the pan of weight 15 g.To make the wire vibrate in 6 loops , find the amount of mass to be removed from the pan (frequency of vibration cons†an t )

Q. In Exercise 14.9, let us take the position of mass when the spring is unstreched as x = 0, and the direction from left to right as the positive direction of x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is (a) at the mean position, (b) at the maximum stretched position, and (c) at the maximum compressed position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?

Q. 18.The ratio of distancesdescribed by a body falling freely from rest in the last second of its motion to that in last but one second of its motion is 5:4 find the toval time taken by the body to reach the ground

Q. 46. a disc of mass m is connected to two springs K1 and K2 as shown. the time period of oscillation is

Q. A weightless rod of length 2l carries two equal masses m ; one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in horizontal position. The speed of the mass B at the instant rod, become vertical is

Q. 50. A 100 g mass stretches a particular spring by9.8 cm, when suspended vertically from it. Howlarge a mass must be attached to the spring if theperiod of vibration is to be 6.28 s?

Q. a 2kg body suspended from a spring of negligible mass is found to streach the spring by 0.1 m if the body is pulled down and the released what is the frequency of the oscillation ​

Q.

Value of spring constant depends upon

1. Elastic properties of the spring

2. Number of turns

3. Length of spring

4. Mass attached to spring

Q. a spring elongated by a length L When a mass M is suspended to it .now a tiny mass m is attached and then released its time period of oscillation is

Q. A particle executes 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. Then its time period in seconds is

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

Q.

Two springs of force constants $K_1$ and $K_2$ are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both $K_1$ and $K_2$ are made four times their original values, the frequency of oscillation becomes:

1. $\frac{f}{4}$
   

2. 4f
   

3. 2f
   

4. $\frac{f}{2}$

Q.

Four blocks and two springs are arranged as shown in figure. The system is at rest. Determine the acceleration of all the loads immediately after the lower thread keeping the system in equilibrium has been cut. Assume that the thread and pulleys are weightless and there is no friction at the point of suspension.

1. = 0

   = 0

   = 0

   upwards

2. = g downloads

   = g downloads

   = g upwards

   upwards

3. = 0

   = 0

   = 0

   upwards

4. = g uploads

   = g uploads

   = g downwards

   downwards

Q. A string of 50cm long is under a tension of 20N force. If mass of string is 1g then frequency of fundamental mode i

Q. A simple pendulum is hanged in a cart and cart is sliding on inclined plane of inclination 60^° , with horizontal. If friction has no role, then time period of oscillation will be (here, I is length of simple 81 (1) 2u (2) 3/ (4) 2g 21 31

Q. Molten-wax of mass $m$ drops on a block of mass $M$, which is oscillating on a frictionless table. Select the correct option.

1. time period does not change
2. amplitude increases
3. time period decreases
4. time period increases

Q. A simple harmonic oscillator having four identical springs as shown in figure has time period (neglect the separation between the ends on the roof and the ends connected to the mass):

1. $2\pi \sqrt{\frac{m}{4k}}$
2. $2\pi \sqrt{\frac{m}{2k}}$
3. $2\pi \sqrt{\frac{m}{k}}$
4. $2\pi \sqrt{\frac{m}{8k}}$

Q. 8.A homogenous rod XY of length L mass M is pivoted at the centre C such that it can rotate freely in vertical plane . Initially the rod is in horizontal posIiton. A blob of same mass M as that of rod , falls vertically with speed V and sticks rod midway between C and Y . If rod rotated with angular speed w what will be angular speed in terms of V and L ?

Q. A block of mass m is connected with two springs connected in parallel combinatio, each of mass 2m and spring constants 2k as . The angular frequency of SHM performed by the block will be

Q. a 1 kg block is executing SHM of amplitude 0.1 m in a vertical plane under restoring force of spring constant 100 N/m a block of mass 24 kg is at rest collides inelastically with the oscillating block of 1 kg and stick to it at the instant it passes through the mean position find out the frequency of oscillation of combined mass

Q. A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended with its length vertical from a fixed point by a massless spring $($spring constant $k)$ such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_o$ of the spring when it is in equilibrium is:

1. $\frac{Mg}{k}(1+\frac{LA\sigma }{M})$
2. $\frac{Mg}{k}(1-\frac{LA\sigma }{2M})$

3. $\frac{Mg}{k}$

4. $\frac{Mg}{k}(1-\frac{LA\sigma }{M})$