Simple harmonic motion Questions and Answers

A 1 00 x 10 2 kg particle is vibrating in simple harmonic motion with a time period of 1 00 x 10 5 sec and a maximun speed of 1 00 x 10 3 m s The maximum displacement of th particle is 1 59 nm 1 59 m 1 59 mm None of these

23 A particle is undergoing simple harmonic motion on a straight line of amplitude 1 cm and time period 8 second Starting from mean position the distance covered by the particle in first five seconds is approximately 1 2 1 cm 3 2 5 cm 2 2 3 cm 4 2 7 cm dations

A wedge of mass m is kept on smooth surface and connected with two springs as shown in the figure Initially springs are in their natural length Time period of small oscillations of the wadge will be fr eeeee 4k 60 m k Jeeee KV

A plane wave is represented by x 1 2 sin 314t 12 56y Where x and y are distances measured along in x and direction in meters and t is time in seconds This wave has A wavelength of 0 25 m and travels in ve x direction A wavelength of 0 25 m and travels in ve y direction A wavelength of 0 5 m and travels in ve y direction A wavelength of 0 5 m and travels in ve x direction

2 Two pendulums have time period T and 5T 4 They starts SHM at the same time from the mean position What will be the phase difference between them after the bigger pendulum completed one oscillation a 45 c 60 b 90 d 30

A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all direction The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm fixed at its mid point The bob is displaced slightly perpendicular to the plane of the rod and string Find period of small oscillations of the system in the form X And fill value of X g 10m s sec 10 B 1 20 cm Bob

1 A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is T When the sphere is immersed in a non viscous liquid of density 1 10 that of brass it will act as a simple pendulum of period a T 10 b T 9 C 9 10 T d 10 T

6 Two linear simple harmonic motion of equal amplitude a frequencies 20 are impressed on a particle along x y axis respectively resultant path followed by particle is given by x y a What is initial phase difference between them A B IN 3x D

3 The relation between acceleration and displacement of four particles are given below a a 2x C c a 2x b a ax d a 2x 2x Which one of the particle is exempting simple harmonic motion

15 When the kinetic energy of a body executing SHM is 1 3 of the potential energy The displacement of the body is x percent of amplitude where x is a 51 b 87 c 73 d 13 6 How long after the beginning of motion ie 1 S 2 F 3

In the overhead view of above figure a long uniform rod of mass 0 600kg is free to rotate in a horizontal plane about a vertical axis through its center A spring with force constant k 1850N m is connected horizontally between one end of the rod and a fixed wall When the rod is in equilibrium it is parallel to the wall What is the period of the small oscillations that result when the rod is rotated slightly and released Wall oooo

7 The motion of a particle executing simple harmonic motion is described by the displacement function x t A cos wt p If the initial t 0 position of the particle is 1 cm and its initial velocity is cm s what are its amplitude and initial phase angle The angular frequency of the particle is ns If instead of the cosine function we choose the sine function to describe the SHM x B sin at a what are the amplitude and initial phase of the particle with the above initial conditions fuam 0 to 50 kg The length of the scale is 20

As shown in the figure the spring mass system is subjected to Simple Harmonic Motion The time period is T 12s Determine the time taken by the mass to reach half of the amplitude from the mean position k mmmmmm A 1s B 2s m A

21 If the two S H M s are having same period along same path and amplitude is same but different initial phases the resultant amplitude when two S H M s are out of phase n is a double b same c zero d infinity

A homogeneous disk is allowed to swing in a vertical plane about the pivot shown below Compute the following quantities showing steps in detail don t copy ready formulas 1 The moment of inertia about the center of mass by direct integration 2 The moment of inertia about the pivot 3 The radius of gyration about the pivot 4 The period of oscillations 5 The center of oscillations for the pivot Pivot

A uniform rod of length 6m is hanged vertically from one end and given a small angular displacement from mean position then it starts performing angular SHM calculate the time period of that SHM Take g