Amplitude, Frequency, Wave Number, Phase Shift

         

A body of mass m=2 kgm = 2\text{ kg} is oscillating on a spring. The position in meters of the body as a function of time tt can be expressed as

x(t)=Acos(2πft) m. x(t) = A\cos{(2\pi ft)} \text{ m} .

If the phase of x(t) x(t) is shifted by δ=8π5 rad,\delta = \frac{8 \pi}{5} \text{ rad}, the time delay of its cycle is KT s,KT \text{ s}, where TT is the period of the oscillation. What is the constant K?K?

A body of mass m=2 kgm = 2\text{ kg} is oscillating on a spring. The position of the body in meters as a function of time tt can be expressed ass x(t)=Acos(2πft) m. x(t) = A\cos{(2\pi ft)} \text{ m}. If x(t) x(t) is delayed by 13\frac{1}{3} of its cycle, what is the phase shift δ\delta in radians?

As illustrated in the above diagram, a body of mass m=4 kgm = 4 \text{ kg} attached to a spring with spring constant k=16 N/m k = 16 \text{ N/m} is oscillating on a frictionless floor. Initially at t=0,t=0, the position of the body was x(t=0)=4 m  x(t=0) = 4 \text{ m } and the velocity was v(t=0)=0 m/s . v(t=0) = 0 \text{ m/s }. What is the amplitude of the oscillation?

A body of mass m=2 kgm = 2 \text{ kg} is oscillating on a spring. The position of the body is given as x(t)=4cos(30t) m, x(t) = 4 \cos{(30 t)} \text{ m}, where xx denotes the difference in the length of the spring from its original length. What is the period of the body?

Assume that π=3\pi = 3 .

A normal human can hear the sound frequency from 20 Hz 20 \text{ Hz} to 20000 Hz. 20000 \text{ Hz}. Find the longest wavelength of the hearable sound, given that the speed of sound is 340 m/s. 340 \text{ m/s}.

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