Answer to Question #193739 in Mechanics | Relativity for Rocky Valmores

Question

  A mass m=2kg hangs from a spring of spring constant 400 N/m. The spring is stretched 0.25m from its equilibrium position and then released. Use the Lagrangian to determine the vertical velocity of the block at t = 5s.

Answer 1

m=2kg

K=400 N/m

A=0.25m

$\omega =\sqrt{K\over m}$

$\omega =\sqrt{400\over 2}=20 \ rad/s$

X=Asin(wt)

X=0.25sin(20t)

We get Velocity at any time t by using lagrangian differentiation

V=0.25cos(20t)

At t= 5 s

V= 0.25cos(100rad)

V=0.215 m/s