Part 1: A support beam, within an industrial building, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the bear. The displacement caused by the vibrations can be modelled by the following equations, x₁ = 4.2 sin(100nt +0.59) mm x₂ = 6.1 sin(100mt-0.42) mm Your senior engineer asked you the followings: (a) State the amplitude, periodic time, frequency and phase angle (in degrees) for each of these waves.

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Part A The position of an object that is oscillating on an ideal spring is given by the equation z = (a) At time t =0.815 s, how fast is the object moving? (12.3 cm) cos[(1.26s-1)t]. cm/s Submit Request Answer Part B (b) At time t = 0.815 s, what is the magnitude of the acceleration of the object? ΑΣφ cm/s2 Submit Request Answer

Question 2 ) = – 5 and y (0) = 5. An object is in simple harmonic motion with frequency 6. Suppose y(0) Find its displacement for t> 0. Also, find the amplitude of the oscillation and the sine and cosine of the initial phase angle o. Displacement: y(t) Amplitude sin(ø) cos(ø) =

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Problem 2:  Special sections of roadway are sometimes paved with “rumble strips” to alert inattentive drivers. In a particular case the grooves are spaced L = 0.26 m apart and the depth of each groove is d = 0.35 cm. As you drive over this rumble strip, the tires of your car oscillate about their equilibrium positions with a frequency of f = 68.6Hz. Refer to the figure, which is not drawn to scale.  Part (b) Find the vertical position of the tire, in centimeters, at the time t = 1.85 s. Part (c) With your tire oscillating at a frequency of f = 68.6 Hz and the distance between grooves L = 0.26 m, what is the speed of your car, in kilometers per hour?

Problem 3: An object is undergoing simple harmonic motion along the x-axis. Its position is described as a function of time by x(t) = 1.7 cos(3.1t – 1.3), where x is in meters, the time, t, is in seconds, and the argument of the cosine is in radians. Part (a) Find the amplitude of the simple harmonic motion, in meters. Part (b) What is the value of the angular frequency, in radians per second? Part (c) Determine the position of the object, in meters, at the time t = 0. Part (d) What is the object's velocity, in meters per second, at time t = 0? Part (e) Calculate the object's acceleration, in meters per second squared, at time t = 0. Part (f) What is the magnitude of the object's maximum acceleration, in meters per second squared?

Create a plot of the period vs. mass (exclude the steel bolt). Construct your plot on a computer program such as Microsoft Excel®.

At an outdoor market, a bunch of bananas is set into oscillatory motion with an amplitude of 20.0 cm on a spring with a force constant of 16.0 N/m. It is observed that the maximum speed of the bunch of bananas is 43.0 cm/s. What is the weight of the bananas in newtons? N

A complete description of simple harmonic motion must take into account several physical quantities and various mathematical relations among them. This information is needed to solve oscillation Part A problems of this type. The position of a 40 g oscillating mass is given by x(t) = (2.0 cm) cos(10t), where t is in seconds. Determine the velocity at t = 0.40 s. Express your answer in meters per second to two significant figures. • View Available Hint(s) ? Vr = m/s Submit Part B 國 t