A mass on a string of unknown length oscillates as a pendulum with a period of 4.00 s. What is the period if a. The mass is doubled? b. The string length is doubled? c. The string length is halved? d. The amplitude is halved? Parts a to d are independent questions, each referring to the initial situation.?

a) T= 4.00s

b)T = 5.66s

c)T  = 2.83s

d)T = 4.00s

Explanation:

a)  The pendulum period is express as

The period does not depend on the mass and depend only on the length

so we have,

b) for new length

so, we have

c) For a new length

d) the period does not depend on the amplitude as long as there is simple harmonic motion

so, we have

T = 4.00s

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm