Advertisements
Advertisements
प्रश्न
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
उत्तर
(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
संबंधित प्रश्न
A seconds pendulum is suspended in an elevator moving with constant speed in downward direction. The periodic time (T) of that pendulum is _______.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
General vibrations of a polyatomic molecule about its equilibrium position.
Figure depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?
The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?
Answer in brief:
Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?
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
The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitude 2 cm, 1 m s−1 and 10 m s−2 at a certain instant. Find the amplitude and the time period of the motion.
Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.
The string the spring and the pulley shown in figure are light. Find the time period of the mass m.
Find the time period of the motion of the particle shown in figure . Neglect the small effect of the bend near the bottom.
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?
Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10-5 Wb/m2. The magnet has a moment of inertia 3 × 10-6 kg/m2 and magnetic moment 3 A m2.
A simple pendulum is inside a spacecraft. What will be its periodic time?
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
The rotation of the earth about its axis.
A simple pendulum of frequency n falls freely under gravity from a certain height from the ground level. Its frequency of oscillation.
The displacement time graph of a particle executing S.H.M. is shown in figure. Which of the following statement is/are true?
- The force is zero at `t = (T)/4`.
- The acceleration is maximum at `t = (4T)/4`.
- The velocity is maximum at `t = T/4`.
- The P.E. is equal to K.E. of oscillation at `t = T/2`.
What are the two basic characteristics of a simple harmonic motion?
A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.
- Will there be any change in weight of the body, during the oscillation?
- If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?
