Question

Two physical pendulums (not simple pendulums) are made from meter sticks that are suspended from the ceiling at one end. The sticks are uniform and are identical in all respects, except that one is made of wood (mass=0.36 kg) and the other of metal (mass=0.82 kg) They are set into oscillation and execute simple harmonic motion. Determine the period of (a) the wood pendulum and (b) the metal pendulum

Answer 1

a) T = 0.579 s , b) T = 0.579 s

Step-by-step explanation:

The great advantage of wave mechanics is that the general equations for different systems are the same, what changes are the physical parameters involved, the equation of motion is

x = A cos (wt +φ)

Where w is the angular velocity that is this case for being a solid body is

w = √ (mg d / I)

Where I is the moment of inertia and d the distance to the pivot point

The moment of inertia for a ruler hold one end is

I = 1/12 M L²

The lost is related to the frequency and is with the angular velocity

T = 1 / f

w = 2π f

w = 2π / T

T = 2π / w

T = 2π √ I / mgd

For our case

d = L

T = 2π √(1/12 M L²) / M g L)

T = 2π √(L/(12 g))

a) wood suppose it is one meter long (L = 1m)

T = 2π √ (1 / (12 9.8))

T = 0.579 s

b) metal length (L = 1m)

T = 2pi RA (1 / (12 9.8))

T = 0.579 s

The period does not depend on mass but on length