Question

Consider a simple harmonic oscillator made of a mass sliding on a frictionless surface, and attached to a massless linear spring. Which of the following statements are true? (If A and E are, and the others are not, enter TFFFT).

     A) Doubling the mass will not change the period.
     B) Doubling the amplitude will halve the frequency.
     C) Quadrupling the spring constant will double the frequency.
     D) Doubling the mass will double the frequency.
     E) Tripling the spring constant will sextuple the period.

Thank you for your help

Answer 1

as we know the equations..

ω=2 pi (frequency )=1/time-period = √(k/m).....(1)

and x(t)=Acos(ωt+ϕ) ....(2)

from equation 1

A. doubling the mass period will root 2 from equation 1 SO false

B. amplitude and frequency are not dirrectly related as we can see from equation 2 so false

C. 4 time of k in root will 2 times of frequency from equation 1. so correct option

D. double the mass will 1/√2 so wrong option

E. triple K it will 1/√ 3 so wrong option.

answer is FFTFF