Question

Part A

A block of unknown mass is attached to a spring with a spring constant of 5.50 N/m and undergoes simple harmonic motion with an amplitude of 10.0 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 28.0 cm/s.

(a) Calculate the mass of the block.

________kg

(b) Calculate the period of the motion.

________s

(c) Calculate the maximum acceleration of the block.

________m/s^{2}

^{Part B}

A block-spring system oscillates with an amplitude of 3.65 cm. The spring constant is 250 N/m and the mass of the block is 0.300 kg.

(a) Determine the mechanical energy of the system.

__________J

(b) Determine the maximum speed of the block.

__________m/s

(c) Determine the maximum acceleration.

_________m/s^{2}

Answer #1

a) when the mass is half way the displacement x= 5 cm

PE(spring) = 0.5 kx^{2} = 0.5*5.5*0.05^{2} =
6.875e-3

This equal to the KE of the mass = 0.5mv^{2} =
0.5m*0.28^{2}

m = 6.875e-3/(0.5*0.28^{2} ) = 0.175 kg

b) period T = 2
= 2*3.14*(0.175/5.5)^{1/2} = 1.68 s

c) acceleration a = (k/m)*x

= (5.5/0.175)*0.1 = 3.143 m/s^{2}

d) maximum speed v = A =
0.1*(5.5/0.175)^{1/2} = 0.56 m/s

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