a mass m is attached to the end of a spring (constant k) as shown below. the mas

Question

a mass m is attached to the end of a spring (constant k) as shown below. the mass is given an initial displacement x0 from equilibrium, and an initial speed v0.

Ignoring friction and the mass of the spring, use energy methods to find the following in terms of the given quantities. (Use any variable or symbol stated above as necessary.)

(a) its maximum speed vmax =

(b) its maximum stretch from equilibrium xmax =

Explanation / Answer

a)vo xo E=.5kxo^2+.5mv^2 for vmax E spring=0 =>.5mvmax^2=.5kx0^2+.5mv0^2 =>Vmax=sqrt((k/m)xo^2+vo^2) for xmax ke=0 .5k xmax^2=.5kx0^2+.5mv0^2 =>xmax=sqrt(xo^2+(m/k)Vo^2)

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