#46 The length of a simple pendulum is 0.79 m and the mass of the particle The p

Question

#46

The length of a simple pendulum is 0.79 m and the mass of the particle The pendulum is pulled away from its equilibrium by an angle of 8.50 degreee released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. What is the angular frequency of the motion? Using the position the at its lowest point at the reference level, determine the mechanical energy of the pendulum as it swings back and What is the speed as it passes through the lowest point at the swing? A simple pendulum is swinging back and through a angle, its motion repeating every 1.25 s. How much longer should the pendulum be made in increase

Explanation / Answer

let L is the actula length of the pendulum

we know, T = 2*pi*sqrt(L/g)

T^2 = 4*pi^2*L/g

==> L = g*T^2/(4*pi^2)

= 9.8*1.25^2/(4*pi^2)

= 0.3878 s

new time period, T' = 1.25 + 0.2 = 1.45 s

so, new length of the pensulum, L' = g*T'^2/(4*pi^2)

= 9.8*1.45^2/(4*pi^2)

= 0.5219 m

so, increase in length of the pendulum = L' - L

= 0.5219 - 0.3878

= 0.1341 m

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