Define Linear S.H.M. - Physics


Define linear S.H.M.



Linear S.H.M. is defined as the linear periodic motion of a body in which the restoring force (or acceleration) is always directed towards its mean position and its magnitude is directly proportional to the displacement from the mean position.
Consider a particle ‘P’ moving along the circumference of a circle of radius 'a' and centre O, with uniform angular speed of 'ω' in anticlockwise direction as shown.
Particle P along circumference of the circle has its projection particle on diameter AB at point M.


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2015-2016 (March)


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A particle performing linear S.H.M. has a period of 6.28 seconds and a pathlength of 20 cm. What is the velocity when its displacement is 6 cm from mean position?

The maximum velocity of a particle performing linear S.H.M. is 0.16 m/s. If its maximum acceleration is 0.64 m/s2, calculate its period.

Two particles perform linear simple harmonic motion along the same path of length 2A and period T as shown in the graph below. The phase difference between them is ___________.

Obtain the differential equation of linear simple harmonic motion.

A particle executing linear S.H.M. has velocities v1 and v2 at distances x1 and x2 respectively from the mean position. The angular velocity of the particle is _______

A particle performing linear S.H.M. has the maximum velocity of 25 cm/s and maximum acceleration of 100 cm/ m2. Find the amplitude and period of oscillation. (π = 3.142)

From differential equation of linear S.H.M., obtain an expression for acceleration, velocity and displacement of a particle performing S.H.M.

In SI units, the differential equation of an S.H.M. is `("d"^2"x")/("dt"^2)` = − 36x. Find its frequency and period.

A body of mass m performs linear S.H.M. given by equation, x = P sin cot + Q sin`(omega"t" + pi/2)`. The total energy of the particle at any instant is ______.

A particle performing Linear S.H.M. has a maximum velocity 25 cm/sand maximum acceleration 100 cm/s2. Find the period of oscillations.

What is the rotational analogue of Newton's second law of motion?

The speeds of a particle performing linear SHM are 8 units and 6 units at respective displacements of 6 cm and 8 cm. Find its period and amplitude.

A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released osillates with a period of 0.6 sec. What is the weight of the body?


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