Simple harmonic motion Questions and Answers

37 The shortest distance travelled by a particle executing S H M from 3 2 its mean position in 2 seconds is of its amplitude Find its Ans 0 21 s period 38 At what displacement the velocity of the body executing S H M is half that at equilibrium position

d 180 290 A boy throws a ball upwards with velocity vo 20m s The L e 90 2 wind imparts a horizontal acceleration of 4 m s to the left The angle 0 at which the ball must be thrown so that the ball returns to the boy s hand is g 10 m s a tan 1 2 c tan 2 291 There are two values of t b tan 0 2 0 4 1 d tan Rotate

Case 2 Equilibrium of a current carrying conductor When a finite length current carrying wire is kept parallel to another infinite length current carrying wire it can suspend freely in air as shown below Movable Fixed mg X 40 Magnetic Effect of Current 12 h Y Downloaded from ToraLabs proof In both the situations for equilium of XY it s downward weight upward magnetic force i e Mo 21 12 1 4 T h Note In the first case if wire XY is SHM and it s time period is give by T 27 h Fixed g Movable lac from its equilibrium position it executes

A heavy block is attached to the ceiling by a spring that has a force constant k A conducting rod is attached to block The combined mass of the block and the rod is m The rod can slide without friction along two vertical parallel rails which are a distance L apart A capacitor of known capacitance C is attached to the rails by the wires The entire system is placed in a uniform magnetic field B Find the time period T of the vertical oscillations of the block Neglect the electrical resistance of the rod and all wires rail x X x X rail

A simple pendulum of length L is constructed from a point object of mass m suspended by a massless string attached to a fixed pivot point A small peg is placed a distance 2L 3 directly below the fixed pivot point so that the pendulum would swing as shown in the figure below The mass is displaced 5 degrees from the vertical and released How long does it take to T return to its starting position T The value of L fixed pivot point small peg point object

c 384 Hz d 500 Hz 29 A particle executes SHM with an amplitude of 2 cm When the particle is at 1 cm from the mean position the magnitude of its velocity is equal to that of its acceleration Then its time period in seconds is b 2n 3 d 2n 3 2 c 3 2 50 A body of mass m thrown horizontally with velocity

3 The maximum velocity of a particle executing simple harmonic motion is v If the amplitude is doubled and the time period of oscillation decreased to 1 3 of its original value the maximum velocity becomes a 18v b 12v c 6v d 3v

When displaced and released the 2 kg mass in figure oscillates on the frictionless horizontal surface with period 6 seconds If a small mass is placed on the 2 kg block and the coefficient of static friction between the small mass and the 2 kg block is 0 1 then the maximum amplitude of oscillation before the small mass slips is A 10 m Assume the period is unaffected by adding the small mass Then value of A is k 100000 m 2kg

In simple harmonic motion Which one of the following quantities has constant ratio with acceleration A Time B Displacement C Velocity Mass Medium

y A 55 P t 0 X Fig 14 10 P t 0 B T 30 s Example 14 4 Fig 14 10 depicts two circular motions The radius of the circle the period of revolution the initial position and the sense of revolution are indicated on the figures Obtain the simple harmonic motions of the x projection of the radius vector of the rotating particle P in each case

In the given figure a mass M is attached to a horizontal spring which is fixed on one side to a rigid support The spring constant of the spring is k The mass oscillates on frictionless surface with time period T and amplitude A When the mass is in equilibrium position as shown in the figure another mass m is gently fixed upon it The new amplitude of oscillations will be 4 M oooooooo k

154 1 The displacements of the particle from the extreme position when its kinetic energy is th of 3 the maximum value and th of the maximum value are XA XA and X respectively The ratio is XB 1 3 1 2 1 2 3 1 3 4 2 3 1 155 15

a block of mass 200 g falls from a height of 9 8 cm on the pan of a spring balance as shown the mass of the pan and spring is negligible the block gets stuck to the pan and starts oscillting simple harmonically in the vertical direction the energy of its oscillation is O 0 1931 O 193 O 19 3j 00103

Motion 11 A simple pendulum has a length of 13 m and mass 25 kg The pendulum bob is pulled 0 5 m to one side from its rest position and releas Calculate the maximum acceleration experienced by the bob in m s 2

Problem 4 7 When the masses of the coupled pendulums of Figure 4 1 are no longer equal the equations of motion become 100 and m x m g l x s x y m y m g l y x x y Show that we may choose the normal coordinates Coupled Oscillations mix m y m m with a normal mode frequency w g l and Y x y with a normal mode frequency X

Figure shows the kinetic energy K of a simple pendulum versus its angle 0 from the vertical The pendulum bob has mass 0 2 kg The length of the pendulum is equal to g 10 m s auf Kaen Jefers 0 2 Rada RR g 10 100 A 2 0 m K MJ 15 10 0 B 1 8 m 100 0 mrad C 1 5 m D 1 2 m