Answer to Question #249965 in Mechanics | Relativity for Hloni

Question #249965
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?
1
Expert's answer
2021-10-11T16:45:00-0400

1)

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

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

2)

sinωt=xA,\sin \omega t=\frac xA,

cosωt=A2x2A,\cos \omega t=\frac{\sqrt{A^2-x^2}}A,

v=Aωcosωt=ωA2x2=8.3 ms,v=A\omega\cos \omega t=\omega \sqrt{A^2-x^2}=8.3~\frac ms,

3)

a=Aω2sinωt=xω2=105 ms2,a=-A\omega^2\sin \omega t=-x\omega^2=-105~\frac m{s^2},

4)

F=kx=84 N.F=-kx=-84~N.


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