Question

A 1.25 kg block is attached to a spring with spring constant 13.0 N/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 36.0 cm/s . What are

Part A

The amplitude of the subsequent oscillations?

Express your answer with the appropriate units.

Part B

The block's speed at the point where x= 0.400 A?

Express your answer with the appropriate units.

Answer 1

Initial energy of spring mass system Ei = (1/2)*m*v^2

final energy after compression Ef = (1/2)*k*A^2

From energy conservation

total energy is conserved

Ef = Ei

(1/2)*k*A^2 = (1/2)*m*v^2

A = v*sqrt(m/k)

A = 36*10^-2*sqrt(1.25/13)

A = 0.11 m   <<--------ANSWER

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part B

potential energy at point U = (1/2)*k*x^2

kinetic energy K = (1/2)*m*v^2

total energy E = K + U

but toal energy any point E = (1/2)*K*A^2

K + U = (1/2)*K*A^2

(1/2)*K*x^2 + (1/2)*m*v^2 = (1/2)*K*A^2

Kx^2 + mv^2 + k*A^2

13*(0.4*0.11)^2 + 1.25*v^2 = 13*0.11^2

v = 0.325 m/s <<--------ANSWER