Question

A particle of mass m is executing S.H.M. If amplitude is a and frequency n, the value of its force constant will be:

• A. mn²
• B. 4mn²a²
• C. ma²
• D. 4π²mn²

Answer 1

Answer: (D)

4π²mn²

Answer 2

The force constant (k) in SHM is related to the mass (m) and angular frequency (ω) by $k = mω^2$. The angular frequency (ω) is related to the frequency (n) by $ω = 2πn$. Substituting this relation, we get $k = m(2πn)^2 = 4π^2 mn^2$.