Question

A 2.00 kg block is attached to a spring and force constant of the spring is k = 196 N/m.The block is
held a distance of 5.00 cm from equilibrium and released at t = 0.
(a) Find the angular frequency w, the frequency f, and the period T.
(b) Write an equation for x vs. time.

Answer 1

Gives

K=196N/m

m=2.00kg

x=5.00cm

$w^2=\frac{k}{m}$

Put value

$$w=\sqrt\frac{196}{2}=\sqrt{98}=7\sqrt2rad/sec$$

$f=\frac{w}{2\pi}=\frac{7\sqrt2}{2\pi}Hz$

$T=\frac{2\pi}{w}=\frac{2\pi}{7\sqrt2}$ Sec

Equation

$F=-kx\rightarrow(1)$

$F=m\frac{d^2x}{dt^2}=ma\rightarrow(2)$

Equation (1) and )2) we can written as

$\frac{d^2x}{dt^2}=-\frac{k}{m}x$

$\frac{d^2x}{dt^2}+w^2x=0$