In the differential equation of linear simple harmonic

depicts two circular motions The radius ligure given below of the circle the period of revolution the initial position and the sense of revolution are indicated in the figures Obtain the simple harmonic motions of the x projection of the radius vector of the rotating particle P in each case y T 4s y A 0 45 P t 0 X P t 0 B 0 T 30 s X

extreme position and lowest position are equal The angle 9 of thread deflection in the extreme position will be 1 tan 2 2 tan 2 3 tan 1 2 4 2 tan 1 2

A simple pendulum of length 1 metre suspended from the ceiling of a lift executes oscillation with a period of 6 25 sec If the lift is moving up with an acceleration a find a take g m s e the acceleration of the lift unwards then

smoot and springs are deal If a block of mass m is given the velocity Vo the left direction then the time period of block as shown in the figures is To 31 1 3T K 0000 m K 3 m 2 1 1 m 1 2 2 4 K 0000 3r m 2 VK C m2 1 1

For a particle executing simple harmonic motion the KE is given by K K cos wt Then maximum value of potential energy for given particle 1 May be K 2 Must be K 3 May be less than K 4 Roth 1 3

llustration 18 A simple pendulum of length l is made to oscillate with a solid sphere density D in a non viscous fluid of density p find the period of oscillation D pl

A narrow smooth tunnel of L shapes is made into earth upto central as shown in the figure A small ball which just fits in tunnel is released from A The collision of ball is perfectly inelastic g is acceleration due to gravity on surface of planet 0 RAR 3k Time to fall from A to B is Time to fall from B too T R 2Vg 7 R 4Vg Speed just before hitting B is DSpeed just before hitting O is 4Rg 5 VR Rg 5 VR

Categorise the following function of time cos ot as a S H M b Periodic but not S H M Also find the period Hint cos wf 3 cos wt cos3wt 4

4 8 sec The equation of S H M is y sin 2 nt a then its phase at time t is 1 2nt 2 4 nt 3 2 nt a 4 4 nt 2a A particle executing S H M along y axis has its motion described by the equation y A sinot B the amplitude of S H M is

The young s modulus of material of a thin ring shaped elastic body is Y The mass of ring is m area of cross section is A its initial radius is R Ring is a little elongated then left alone At what time will ring circumference be same as it was initially Neglect loss of energy 1 3 2 TMR 8YA mR YA 2 4 3 2 mR YA KmR V2YA