Question

A block with mass m = 0.3 kg oscillates with amplitude A = 0.4 m at the end of a spring with force constant k = 6 N/m on a frictionless, horizontal surface. Rank the periods of the following oscillating systems from greatest to smallest. If any periods are equal, show their equality in your ranking. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.) (a) The system is as described above. (b) The amplitude is changed to 1.6 m. (c) The mass is changed to 0.6 kg. (d) The spring now has a force constant of 18 N/m. (e) A small resistive force is added so the motion is underdampe

Answer 1

a) T = 1.405 s

b) Period not depends on the amplitude

c) T = 1.987 s

d) T = 0.811 s

e) The period will change by a small value

The rank are:

Tc > Ta = Tb > Te > Td

Step-by-step explanation:

Given:

m = mass = 0.3 kg

A = amplitude = 0.4 m

k = force constant = 6 N/m

a) The time period is:

`T = 2\pi \sqrt{(m)/(k) } =2\pi \sqrt{(0.3)/(6) } =1.405 s`

b) Period not depends on the amplitude

c) Same as a):

`T = 2\pi \sqrt{(m)/(k) } =2\pi \sqrt{(0.6)/(6) } =1.987 s`

d) Same as a):

`T = 2\pi \sqrt{(m)/(k) } =2\pi \sqrt{(0.3)/(18) } =0.811 s`

e) if a small resistive force is added the period will change by a small amount. The rank are:

Tc > Ta = Tb > Te > Td