Simple harmonic motion Questions and Answers

The springs shown are identical When A 4kg the elongation of spring is 1 cm If B 6kg the elongation produced by it is TRO 1 4 cm 3 2 cm rellllle A K K elllllllllllll B 2 3 cm 4 1 cm

Problem 1 21 A block of mass one kg is fastened to a spring with a spring constant 50 Nm The block is pulled to a distance x 10 cm from its equilibrium position at x 0 on a frictionless surface from rest at t 0 Write the expression for its x t and v t Solution Here m 1 kg k 50 Nm A 10 cm 0 10 m k E 1500 m MasT M ICX00 93 00 00 7 07 rad s 65 1 mshin As the motion starts from the mean position so the displacement equation can be written

Two SHM s with same amplitude and time period when acting together in perpendicular directions with a phase difference of r 2 give rise to a straight motion c circular motion b elliptical motion d none of these 1997

3 Maximum 4 Maximum velocity A body oscillates with SHM according to the equation x 5 0 cos 2 t n At time t 2 s its displacement speed and acceleration respectively is 1 0 10 20 3 5 0 20 2 5 0 20 4 5 5m 10 The displacement of a particle in SHM is indicated 4

The x t graph of a particle undergoing simple harmonic motion is shown below The acceleration of the particle of t 4 3 s is 3 cm s AA 0 4 x cm 2 T B 12 s cm s 3 T 23 cm s 4 3 32 cm s r

A block of mass 4 kg is attached to a massless ideal spring and suspended vertically from a ceiling Initially the spring is un stretched when the block is released from rest the Find maximum speed of the block Take spring constan 100 N m and g 10 m s 1 1 m s 3 3 m s ww eeeeeeeee 2 2 m s 4 4 m s

A rod AB of mass m is bent in a shape such that it forms an arc of a circle of radius R The ends A and B of the wire are attached to point O by massless inextensible strings OA and OB If O is the origin X Y are the coordinates of centre of mass of the system and T represents the time period of small oscillations of the system in a plane perpendicular to the plane of OAB then Given angle AOB 60 A X 0 Y 3 3R 2 C T 2n1 R T 3 2 3 3g B X 0 Y D T 2n1 3R 2 RT 3 2 2 I 3 3g A R 1 1 R B

133 A equilibrium towards left and then set free to execute S H M Select correct graph between its velocity v and displacement x 3 4 1 2 f 0 0 0 X X

75 The displacement y of a particle executing periodic motion is given by This expression may be considered to be a result of the superposition of y 4 cos 1 two 3 four sin 1000 t 2 three 4 five independent harmonic motions

A particle is oscillating in a straight line about a centre O with a force directed towards O When at a distance x from O the force is mn x where m is the mass and n is a constant The amplitude is a 15 cm When at a distance 3 from O the particle receives a blow in the direction of motion which generates an extra velocity na If the velocity is away from O at the time of blow and the new amplitude becomes k 3 cm then find k

3 6T 7 4 32 Find the time period of oscillations of a body placed in a tunnel dug into earth any where in the earth approximately 1600 T 2 100 T 3 2 4 10T 10 sec O sec 2 Th Fx Fx 0 1 n 2 22 15 38 The total for in the figure will be 5 5 1 2 3 33 The angular amplitude of a simple pendulum 39 A body of mass a um tension in the string is spring of spring con change in position 2k 2k

13 A particle is executing SHM on a straight line A and Bare two points at which its velocity is zero It passes through a certain point P AP BP at successive intervals of 0 5 s and 1 5 s with a speed of 3 m s a the maximum speed of particle is 3 2 m s b the maximum speed of particle is 2 m s AP 2 1 c the ratio B P 2 1 AP 1 RP d the ratio IS is 2

executing S H M as shown in the figure 1 FA time graph of a particle 3 y to T12 FA 0 The corresponding force time graph of the particle will be 14 T FA 2 o FA T12 t TRA T12 4

A simple pendulum of length 1 m is allowed to oscillate with amplitude 2 It collides elastically with a wall inclined at 1 to the vertical Its time period will be use g Wall 1 2 Jo 20 1 2 3 second goal to 4 3 second 3 2 second 2 211 Je 4 3 2 second 2

A block of mass m is attached to two unstretched springs of spring constants k and k as shown in figure The block is displaced towards right through a distance x and freeee is released Find the speed of the block as it passes through a distance x 4 from its mean position K K seeeeet mheeeeeee

A needle of a sewing machine moves along a path of amplitude 4 cm with frequency 5 Hz Find its acceleration s after it has crossed the mean Ans 34 2 m s 30 position