A simple pendulum of length 1.810 m and mass 1.360 kg is set into motion oscilla

Question

A simple pendulum of length 1.810 m and mass 1.360 kg is set into motion oscillating back and forth. The maximum velocity achieved by the pendulum is 0.7060 m/s. Be sure to use g=9.810 m/s^2
A) from what height was the pendulum released? B) what initial arclength was the pendulum pulled from equilibrium? C) How many oscillations has the pendulum swung through in the first 15 seconds? A simple pendulum of length 1.810 m and mass 1.360 kg is set into motion oscillating back and forth. The maximum velocity achieved by the pendulum is 0.7060 m/s. Be sure to use g=9.810 m/s^2
A) from what height was the pendulum released? B) what initial arclength was the pendulum pulled from equilibrium? C) How many oscillations has the pendulum swung through in the first 15 seconds?
A) from what height was the pendulum released? B) what initial arclength was the pendulum pulled from equilibrium? C) How many oscillations has the pendulum swung through in the first 15 seconds?

Explanation / Answer

from the law of conservation of energy

KE = PE

0.5 mv^2 = mgL(1- cos theta)

here cos theta = (l - h)/l

h = v^2/2g

h = 0.706^2 /(2 * 9.81)

h = 0.025 m

so Cos theta = (1.810 - 0.025)/1810

cos theta = 0.985

theta = 9.93 deg

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arc length = pi R theta/180

arc length = 3.14* 1.81* 9.93/180

arc length = 0.313 m

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T = 2pi sqrt(L/g)

T = 2*3.14* sqrt(1.81/9.81)

T = 2.69 secs

No. of Oscillations = 15/2.69 = 5.57 oscillations

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