Problem 1. Consider the function y = B cos(a x - g t + r) where y and x have units of meters and t has units of seconds. What are the units of B, a, g, and r?
Problem 2. Write down the function y(x) in sine form where y is the displacement as a function of coordinate x, if the spatial frequency of the function is 0.5 7 Π/m, the amplitude of the function is 0.2 m and the function passes through y = 0 with positive slope where x = -1 m.
Problem 3. Consider the function y = (3 m) sin( ( 6Π/m) x + Π/5).
A) What is the amplitude of this function.
B) What is the spatial frequency of this function?
C) What is the spatial period (wavelength) of this function?
D) Sketch this function. Be sure to label and scale the axes and to accurately display where the function passes through the x-axis
Problem 4. Express the function in Problem 3 in
A) cosine form. B) quadrature form.
Problem 5. Analytically find all of the values of x at which the function in Problem 3 has the value y =1 m.
Problem 6.
A) Express the function y = (4 m) cos((10 / s)t) - (3 m) sin((10 / s)t) in cosine form.
B) Express the function y = (4 m) cos((10 / s)t) - (3 m) sin((10 / s)t) in sine form.
Problem 7. Consider the function plotted below.
A) What is the period of the motion?
B) What is the (angular) frequency of the motion in rad/s?
C) Express (approx mately) the function in sine form.
Problem 8. Consider the function y = (2 m) cos ((10/s)t + Π/4). Determine whether each of the following waveforms is equivalent to y? Briefly justify your answers.
1. (2m) sin((10/s)t - Π/4)
2. (2 m) sin((10/s)t + 3Π/4)
3. (2m) cos((10/s) t + 9Π/4)
4. (-2m) cos((10/s) t + 5Π/4)
5. (√2m) [cos((10/s) sin((10/s) t + Π)]