Question

The equation of motion for a particular mass m suspended from a spring of constant k, is:

x=0.40cos(0.70t-0.30)

where x is the displacement of mass from its rest position, t is the time and the phase angle is in radians

From this equation find:

a)The amplitude

b)The frequency of vibration

c)The period

d)The phase angle in degrees

e)The ratio k/m for the spring

Answer 1

$x=0.40\cos(0.70t-0.30),$

a)

$A=0.40,$

b)

$\nu=\frac{\omega}{2\pi}=0.11,$

c)

$T=\frac 1\nu=9,$

d)

$\varphi=\frac{180}{\pi}\varphi_0=17°,$

e)

$\frac km=\omega^2=0.49.$