Question

A simple pendulum of 2 m length is raised 40 cm high and left to oscillate in simple harmonic motion 1. Draw the diagram 2. Calculate the tension in the string when the pendulum is in stationary position. 3. What kind of energy is stored in a pendulum at extreme positions?.Calculate the energy. 4. As the pendulum oscillates through its equilibrium position, calculate its velocity. 5. How much time does it take to complete one Oscillation? 6. How many oscillations will it do in a minute? (Frequency)

Answer 1

Given Length of simple pendulum L km Height of simple pendulum = amplitude of SHM ha= 40cm = A ACO.m. Let mass of the pendulum is . L-A L Img Imgcose ķ 2 Here Q-0.4 Tension in spring is given by T = mgcoso = cos' os (24) ( 2-0 o= cos'(0.8) cos' cos (16) 0736.87° so Tension T= mx 9,8 x cos (36.870) T= 7.84 m . Energy stored in pendulum at extreme positions is the potential energy only and that is given by by P.En P.En mgh 2) PER PELÃ mx g. 8x 014 J P.E.3.924m J LA

4. At the equilibrium position 4 Total energy is due to kinetic energy only SARA SO KE P.E hot =) or = 3.92x.pt -) LD = 3.92*2 = 7.84 m2/52 home Unão = 57.84 mis Vinzo - 2.8 ms $ Time it take to complete on oscillation is period and period of a pendulum is given by T. 97 مه I', TER*3.14 X Barbara = 6-28 x 0.45178 9.2 ) T=4.84 S 6. Frequeng of pendulum is f = + He s' or 0.35 sec => 120.352Hz x 60 sec - 21:13 Oscillatime per minute min fa 21:13 Oscillations per minute