1) The figure below shows the velocity of a simple harmonic oscillator as a func

Question

1) The figure below shows the velocity of a simple harmonic oscillator as a function of time.

(a) Estimate the period.
s

Estimate the magnitude of the maximum velocity.
m/s

Estimate the first time when

v = 0.

s

Calculate the first position after t = 0 when

v = 0.

(Use your estimates.)
m

(b) Calculate the frequency. (Use your estimates.)
Hz

2) The position of a mass-on-a-spring oscillator is given by

y = A sin(35t),

where the value of t is in seconds and

A = 0.39 m.

(a) What is the maximum kinetic energy of an oscillator of mass 2.4 kg?
J

(b) Suppose the amplitude is increased so that the maximum kinetic energy is doubled. What is the new value of A?
m

Explanation / Answer

1)

(a) Estimate the period.
s
period = 0.34- 0.04 = 0.30 s
Estimate the magnitude of the maximum velocity.
m/s

4.0 m/s

Estimate the first time when

v = 0.

s
t = 0.12s
Calculate the first position after t = 0 when

v = 0.

(Use your estimates.)
m
the amplitude of V at maximum x =0, so

t= 0.19s
(b) Calculate the frequency. (Use your estimates.)
Hz

f = 1/T = 1/0.30 = 3.33 Hz

2)

The position of a mass-on-a-spring oscillator is given by

y = A sin(35t),

where the value of t is in seconds and

A = 0.39 m.

(a) What is the maximum kinetic energy of an oscillator of mass 2.4 kg?

maximum ki

= 1/2 m w^2A^2 = 1/2 2.4*(35*0.39)^2 = 223.6 J

J

(b) Suppose the amplitude is increased so that the maximum kinetic energy is doubled. What is the new value of A?
m

A = sqrt(2) *0.39 = 0.551 m

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