If you walk with your arms relaxed and hanging down, they often oscillate forward and back at the same frequency as your stepping frequency. However, if your arms are bent at the elbow so that the forearms are parallel to the ground, they often do not oscillate when you walk. Why? What would you need to do to get them oscillating now? Explain in detail.

The position of an object undergoing simple harmonic motion isgiven by x = A cos1Bt2. Explain the physical significance of theconstants A and B. What is the frequency of this object’s motion?

Adapt the method of Example 6 to determine the amplitude, period, and phase shift for the given function. Graph the function over one period indicating the x- intercepts and the coordinates of the highest and lowest points on the graph. (a) y = 3 cos(7 - 2x) amplitude period phase shift y y 3- 3 3 3 5/7 Зя 4 4 4 4 4 2 o-3 y 4. 4 2 x-intercepts (х, у) - (smaller x-value) (х, у) - (larger x-value) highest points (x, y) = (smaller x-value) (x, y) = (larger x-value) lowest point (x, y) =

96 ۱۲:۳۷ ص © 9 Q Assignment-One Q1- A particle moves in simple harmonic motion with a frequency of 3.00 Hz and an amplitude of 5.00 cm. (a)Through what total distance does the particle move during one cycle of its motion? (b) What is its maximum speed? Where does this maximum speed occur? (c) Find the maximum acceleration of the particle. Where in the motion does the maximum acceleration occur? Q2- For a simple harmonic oscillator, answer yes or no to the following questions. (a) Can the quantities position and velocity have the same sign? (b) Can velocity and acceleration have the same sign? (c) Can position and acceleration have the same sign? Q3- A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is determined. (i) When the elevator accelerates upward, is the period (a) greater, (b) smaller, or (c) unchanged? (ii) When the elevator has a downward acceleration, is the period (a) greater, (b) smaller, or (c) unchanged? (iii) When the elevator…

Near the top of the Citigroup Center building in New York City, there is an object with mass of 3.8 × 105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. a)What effective force constant should the springs have to make them oscillate with a period of 1.4 s in N/m? b)What energy is stored in the springs for a 1.8 m displacement from equilibrium in J?

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There is a web that oscillates horizontally through simple harmonic motion with an amplitude of 2.4 x 10-3 m  and a period of 0.42 seconds. 1. What point(s) of the oscillation does the spider experience a magnitude of acceleration. 2. What is the maximum magnitude of acceleration that the spider experiences?

Q2.A physical pendulum consists of a ring of radius 0.5 m and mass 2 kg. The ring is pivoted at a point on its perimeter. The ring is pulled out such that its centre of mass makes a small initial angle ?0 = 0.2 rad from the vertical and released from rest.  (C) Calculate the angular frequency of the oscillation of the ring (D) Calculate the period of the oscillation of the ring