2. (10 pts) A mass and a spring execute simple harmonic oscillation in which the

Question

2. (10 pts) A mass and a spring execute simple harmonic oscillation in which the position of the mass relative to the equilibrium position) is given by x(t)-(10cm)sin%02s). a) What is the period of the motion (in seconds)? b) What is the frequency of oscillation (in Hz)? c) What is the amplitude of the oscillation? A= 10cm d) Find the spring constant, assuming a mass of 0.50 kg e) What is the total energy of the mass-spring system? f) What will the velocity of the mass be when it is displaced +5 cm from equilibrium?

Explanation / Answer

angular frequency

W=1/0.02 =50 rad/sec

Period

T=2pi/W =2pi/50=0.12566 s

b)

frequency

f=1/T =1/0.12566=7.958 Hz

c)

amplitude of oscillation

A=10 cm

d)

spring constant

K=mW2=0.5*502

K=1250 N/m

e)

Total energy

E=(1/2)KA2=(1/2)*1250*0.12=6.25 J

f)

V=W*sqrt(A2-X2)=50*sqrt(0.12-0.052)

V=4.33 m/s

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