Question

**#1: A mass of 6 kg is attached to a spring with k = 1500
N/m. It is stretched a distance of 0.5 m and is released so that it
oscillates in simple harmonic motion.**

**A)** What is the frequency?

**B)** What is the energy of the oscillator?

**C)** What is the maximum velocity for the
oscillator?

**#2: When at x = 0.3 m a simple harmonic
oscillator (k = 2000 N/m and m = 2 kg) has a velocity of 8
m/s.**

**A)** What is the Amplitude?

**B)** What is the frequency of the oscillator?

**C)** What is the energy of the oscillator?

**D)** What is the maximum velocity for the
oscillator?

**#3: A wave has the form y(x,t) = 0.35 m cos (2 π
m ^{-1} + 400π s^{-1} t).**

**A)** What is the amplitude?

**B)** What is the wavelength?

**C)** What is the frequency?

**D)** What direction is the wave moving?

**E)** What is the magnitude of the velocity of the
wave?

Answer #1

Multiple questions posted, so answering only the first question:

1.

A) Frequency of spring mass system is given by: 1/(2)* (k/m)1/2 , where k is spring constant and m is mass.

Here,k=1500 N/m, m=6 kg.

So,frequency = 1/(2)* (1500/6)1/2 = 2.516 Hz.

B) At the extreme position, total energy energy = potential energy.

For spring, potential energy=1/2kx2, where k is spring constant and x is compression/elongation of the spring.

Here,k=1500 N/m and x=0.5 m.

So, energy = 1/2*1500*0.5*0.5 = 187.5 J

C) Maximum velocity occurs at mean position, where kinetic energy= total energy

Kinetic energy = 1/2mv2, where m is mass and v is velocity.

So, for maximum velocity, kinetic energy= total energy => 1/2*6v2 = 187.5 =>v2 = 187.5/3 = 62.5

=>v=7.906 m/s.

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