A small mass attached to a spring oscillates with simple harmonic motion with amplitude of 70mm,taking 13 seconds to make 40 complete oscillations.Calculate the following showing steps;

Question

a.Its angular ferquency
b.Its maximum speed
c.Its maximum acceleration
d.Its speed when displacement from equilibrium is 10mm
e.Its speed when displacement from equilibrium is 20mm

Answer 1

ΔT = t/N = 13/40 = 0.325 s.
a.
ω = 2•π/T = 2•π/0.325 = 19.33 rad/s.
b.
v(max) = A•ω= 70•10^-3•19.33 = 1.353 m/s
c.
a(max) =A•ω^2 = 26.16 rad/s^2.
d.
x= A•cos(ω•t+α) = 10 mm
cos(ω•t+α) = x/A= 10/70 =1/7.
sin(ω•t+α) = sqrt(1 – (cos(ω•t+α))^2) = 0.9897,
v = - A• ω• sin(ω•t+α) = 70•10^-3•19.33•0.9897 = -1.34 m/s.
e. similar to "d".