Advertisements
Advertisements
Question
A particle of mass m is attatched to three springs A, B and C of equal force constants kas shown in figure . If the particle is pushed slightly against the spring C and released, find the time period of oscillation.
Advertisements
Solution
(a) Let us push the particle lightly against the spring C through displacement x.
As a result of this movement, the resultant force on the particle is kx.
The force on the particle due to springs A and B is \[\frac{kx}{\sqrt{2}}\] .
Total Resultant force \[= kx + \sqrt{\left( \frac{kx}{\sqrt{2}} \right)^2 + \left( \frac{kx}{\sqrt{2}} \right)^2}\]
= kx + kx = 2kx
Acceleration is given by \[= \frac{2kx}{m}\]
\[\text { Time period }= 2\pi\sqrt{\frac{\text { Displacement }}{\text { Acceleration }}}\]
\[ = 2\pi\sqrt{\frac{x}{2kx/m}}\]
\[ = 2\pi\sqrt{\frac{m}{2k}}\]
APPEARS IN
RELATED QUESTIONS
A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x108 N is applied to a top surface. Calculate the lateral displacement of the top surface if modulus of rigidity of copper is 14x1010 N/m2.
Answer in brief:
Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?
The length of the second’s pendulum in a clock is increased to 4 times its initial length. Calculate the number of oscillations completed by the new pendulum in one minute.
A person goes to bed at sharp 10.00 pm every day. Is it an example of periodic motion? If yes, what is the time period? If no, why?
A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates is
Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant k1 and k2 respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is
A particle moves in a circular path with a uniform speed. Its motion is
A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is
The string the spring and the pulley shown in figure are light. Find the time period of the mass m.
The left block in figure moves at a speed v towards the right block placed in equilibrium. All collisions to take place are elastic and the surfaces are frictionless. Show that the motions of the two blocks are periodic. Find the time period of these periodic motions. Neglect the widths of the blocks.
A uniform disc of radius r is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?
A body of mass 1 kg is mafe to oscillate on a spring of force constant 16 N/m. Calculate (a) Angular frequency, (b) Frequency of vibrations.
The period of oscillation of a body of mass m1 suspended from a light spring is T. When a body of mass m2 is tied to the first body and the system is made to oscillate, the period is 2T. Compare the masses m1 and m2
Which of the following example represent periodic motion?
A swimmer completing one (return) trip from one bank of a river to the other and back.
Which of the following example represent periodic motion?
A freely suspended bar magnet displaced from its N-S direction and released.
The equation of motion of a particle is x = a cos (αt)2. The motion is ______.
What are the two basic characteristics of a simple harmonic motion?
The time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration `g/2`, the time period of the pendulum will be ______.
