2. A rope of 2 meters long is tied to the roof and at the other end a mass of 1

Question

2. A rope of 2 meters long is tied to the roof and at the other end a mass of 1 kg is fixed. , then it moves 10 degrees from its equilibrium point and is left free. a) Determine the period and frequency of oscillation. If this system is carried to the moon, where gravity is 1/6 the gravity of the Earth. b) what will be your new period and frequency of oscillation.

3. To study the behavior of the waves, take a cable 4Kg mass and 20 m long, this is attached to an oscillator, and the other end is passed by a fixed pulley that is 16 m from the oscillator. At the free end, 40 kg are hung and the oscillator starts to work. It is observed that 15 waves are formed with an amplitude of 30 cm. Determine: a) the speed of the waves, b) the length of the waves formed, c) the frequency, d) the energy per unit length, e) the power. For that system, f) what will be the fundamental frequency and the seventh over-tone?
2. A rope of 2 meters long is tied to the roof and at the other end a mass of 1 kg is fixed. , then it moves 10 degrees from its equilibrium point and is left free. a) Determine the period and frequency of oscillation. If this system is carried to the moon, where gravity is 1/6 the gravity of the Earth. b) what will be your new period and frequency of oscillation.

3. To study the behavior of the waves, take a cable 4Kg mass and 20 m long, this is attached to an oscillator, and the other end is passed by a fixed pulley that is 16 m from the oscillator. At the free end, 40 kg are hung and the oscillator starts to work. It is observed that 15 waves are formed with an amplitude of 30 cm. Determine: a) the speed of the waves, b) the length of the waves formed, c) the frequency, d) the energy per unit length, e) the power. For that system, f) what will be the fundamental frequency and the seventh over-tone?

3. To study the behavior of the waves, take a cable 4Kg mass and 20 m long, this is attached to an oscillator, and the other end is passed by a fixed pulley that is 16 m from the oscillator. At the free end, 40 kg are hung and the oscillator starts to work. It is observed that 15 waves are formed with an amplitude of 30 cm. Determine: a) the speed of the waves, b) the length of the waves formed, c) the frequency, d) the energy per unit length, e) the power. For that system, f) what will be the fundamental frequency and the seventh over-tone?

Explanation / Answer

First question -

(a) The period of simple pendulum does not depend on the initial angular displacement.

And the period of a simple pendulum is given by -

T = (1/2*pi)*sqrt(L/g)

pu the values -

T = (1/2*pi)*sqrt(2/9.81) = 0.0719 s

frequency of oscillation, f = 1/T = 1/0.0719 = 13.9 Hz

(b) At the moon, value of g is 9.81/6 m/s^2

So, T = (1/2*pi)*sqrt((2*6)/9.81)) = 0.176 s

frequency of oscillation, f = 1/T = 1/0.176 = 5.7 Hz

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