#4 Please answer the question neatly with steps and show all units, for good rat

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#4
Please answer the question neatly with steps and show all units, for good rating!

Page 2 4. fan Determine the acceleration due to gravity on the surface of the Moon if the period of a simple pendulum whose length is 0.50m is measured to have a period of 3A8sec. on the Moan. (b) What would the period of this same length pendulum on the Earth? suspended (c) A meter stick (whose length is metet of course) and whose Ten-(1/12)ML is from one end as a physical pendulum. What would its period be if its mass is 145grams? s. Given the following equation for the simple harmonic motion exhibited by an object: x (0.30m)cos (12,56tad's)t +*4rad] angle, and the amplitude of (a What are the angular frequency, the frequency, the period, the phase the SHM of the object? What is the position of the object at a time of 0.25sec from t 0? spring (c) What are the velocity and the of the object at this same time? d What is the acceleration constant for the SHM if the mass of the object is 2.0kg? 6. Given a traveling wave described by the equation ular frequency of the tude of the wave, the length of the wave, the ang wave

Explanation / Answer

(a) Time period of oscillations (T) of the simple pendulum is dependent on the length of the pendulum (l) and acceleration due to gravity (g) and is given by

T = 2 (l / g)1/2

T2 = 42 (l/g)

g = 4 2 l / T2

on the surface of the moon it is given that T = 3.48 s and l = 0.5 m

substituting T and l in the above equation

g = 19.71/12.11

g = 1.62 m/s2 on moon

(b) whereas on the surface of earth, g = 9.8 m/s2, hence substituting l and g ,

T = 2 (l / g)1/2

T = 2 * 3.14 * (0.5 / 9.8 ) ½

T = 1.40 s on earth

(C) For a meter stick suspended from one end,

T = 2 (I / m g d)   …….. (1)

Where
"I" is the moment of inertia of the oscillating body of mass "m" wrt to an axis perpendicular to the plane of oscillation passing through the point of suspension,
"d" is the distance between the CM of the oscillating body and the point of suspension. The Center of mass lies at the center of the stick. Hence for a one meter stick , d = 0.5.

Substituting for I = 1/12 mR2, eqn. (1) simplifies to

T = 2 ( m R2 / 12 m g d)1/2 …………. (2) where R = 1m (length of the pendulum)

T = ( 1 / 3 * g * 0.5)1/2   ( g = 9.8 m/s )

T = 0.8 s

This period of oscillations depend only on the length of the pendulum. It does not depend on the mass which is evident from equation(2).

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