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

Question #193739

  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.


1
Expert's answer
2021-05-17T19:01:06-0400

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



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