Question

A massless spring( k= 311N/m) is pulled by 0.5 m from its natural length and released..the spring is attached to a 0.8 kg block and oscillates across a horizontal frictionless surface
1 maximum velocity?
At 0.27m from it natural length, it's
2 velocity will be?
3 acceleration will be?
3 restoring force will be?

Answer 1

1)

$\omega=\sqrt{\frac km}=19.7~\frac{rad}s,$

$v_{max}=A\omega=9.9~\frac ms,$

2)

$\sin \omega t=\frac xA,$

$\cos \omega t=\frac{\sqrt{A^2-x^2}}A,$

$v=A\omega\cos \omega t=\omega \sqrt{A^2-x^2}=8.3~\frac ms,$

3)

$a=-A\omega^2\sin \omega t=-x\omega^2=-105~\frac m{s^2},$

4)

$F=-kx=-84~N.$