1). A 0.20 kg mass resting on a frictionless surface is attached to a solid wall

Question

1). A 0.20 kg mass resting on a frictionless surface is attached to a solid wall by means of a spring with and elastic force constant k of 5.0 N/m. The mass is displaced horizontally from equilibrium a distance of 10.0 cm and released, whereupon the mass undergoes simple harmonic motion. Calculate the following:

a. the oscillation frequency.

b. the total energy of the oscillation.

c. the maximum velocity experienced by the mass.

2.) A fire truck emitting a siren frequency of 1500 Hz speeds by you at 20.0 m/s (~45 mph). Assuming the velocity of sound is 343 m/s, calculate the following:

a. the frequency of the siren as the engine approaches.

b. the frequency of the siren as the engine moves away.

Explanation / Answer

a) f = (1/2*pi)sqrt(5/0.2)=0.796 Hz

b) E = 1/2 k A^2 = 0.5*5*.1^2=0.025 J

c) max v when E = 1/2 mv^2

v = sqrt(2*0.025/.2)=0.5 m/s

2) f = v/(v + vtruck) f0

a) f = 343/(343-20)*1500=1592.8 Hz

b) f=343/(343+20)*1500=1417.4 Hz

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