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.