Civil Engineering MCQAE Level Civil Engineering
A mass m attached to a spring of stiffness k undergoes Simple Harmonic Motion (SHM). Its natural frequency fn (Hz) is:
Engineering MechanicsSHM Natural FrequencyMEDIUM
Choose the correct answer
A
fn = 2pi sqrt(k/m)
B
fn = (1/2pi) sqrt(k/m)
C
fn = sqrt(m/k)
D
fn = k/m
Correct Answer
B. fn = (1/2pi) sqrt(k/m)
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SHM: restoring force F = -kx; equation of motion: m x_double_dot + kx = 0; natural circular frequency omega_n = sqrt(k/m) rad/s; natural frequency fn = omega_n/2pi = (1/2pi)sqrt(k/m) Hz; period T = 1/fn = 2pi sqrt(m/k). For a spring-mass-damper: omega_d = omega_n sqrt(1-zeta^2) (damped frequency).
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