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A simple pendulum has a length L and a mass m. At

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Answer #1

here,

length is l and mass is m

height difference , h = 0.25 * l

let the speed of mass at the lowest point be v

using conservation of energy

0.5 * m * v^2 = m * g * ( h)

0.5 * v^2 = 9.8 * 0.25 * l

v = 2.21 sqrt(l) m/s

----------------------------

y = A * sin(20 * t)

A = 0.44 m

(a)

m = 2.2 kg

maximum speed , vm = A * w

vm = 0.44 * 20 = 8.8 m/s

the maximum kinetic energy of the mass is , KE = 0.5 * m * vm^2

KE = 0.5 * 2.2 * 8.8^2

KE = 85.18 J

(b)

let the new amplitude be A'

maximum speed , vm' = A' * w

vm' = A' * 20

2 * KE = 0.5 * m * vm'^2

2 * 85.18 = 0.5 * 2.2 * (A'*20)^2

A' = 0.62 m

the new amplitude is 0.62 m

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