Question: (a) For a particle moving in simple harmonic motion, the position can be written x(t) = xm cos wt. What is the velocity vx(t) as

(a) For a particle moving in simple harmonic motion, the position can be written x(t) = xm cos wt. What is the velocity vx(t) as a function of time for this particle?
(b) Using the small-angle approximation for the sine function, find the slope of the graph of Φ(t) = Φ0 sin wt at t = 0. Does your result agree with the value of ΔΦ/Δt = wΦ0 cos wt at t = 0?

Step by Step Solution

★★★★★

3.52 Rating (182 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Use Eqs 207a and 207b and the small angle approxim... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

956-P-M-L-M (2536).docx

120 KBs Word File

Students Have Also Explored These Related Mechanics Questions!

The initial position, velocity, and acceleration of an object moving in simple harmonic motion are xi, vi, and ai; the angular frequency of oscillation is w. (a) Show that the position and velocity...

The amplitude of a system moving in simple harmonic motion is doubled. Determine the change in (a) the total energy, (b) the maximum speed, (c) the maximum acceleration, and (d) the period.

A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 2.00 cm, and the...

Hi! I have a quick multiple-choice homework that I'd appreciate any help on. thank you! Part 2: Open-Ended Responses. All work and correct units MUST be shown for full credit. BOX in final answer....

A body is moving in simple harmonic motion with position function 3(t} = 2 + 2 cos t where s is in meters and t is in seconds. Find the jerk at time t. O A. j(t}=0 O B. 55(13): 2cost O C. j(t}=2cost...

A boot.r is moving in simple harmonic motion with position function 3(t} = 2 + 2 cost whore sis in meters and its in seconds. Find the jerk; at time t. D A. j{t}= C! B. t} 2 2co-st O C. j{t}=2cost D...

5. A particle moving in simple harmonic motion has a period, T, of 0.5 seconds, and an amplitude of 30 cm. If it starts at its maximum positive displacement (x = +30cm) at time t = 0.09 find the...

A particle moving in simple harmonic motion passes through the equilibrium point (x=0) 2 times per second. At t=0 its velocity at x=0.04 m is negative. It travels 0.4 m in a complete cycle. The...

1. A 0.3 - kg ball executing a simple harmonic motion has the following displacement as a function of time: x = x cos wt, where the amplitude, Xm = 5.0 m and @ = 4x rad/s. What is the potential...

Project 2: A bead sliding along a rod Simple Harmonic Motion Free Sliding Bead A is constrained to slide along a rod of length . The rod is rotating in a vertical plane beadwith a constant angular...

A tubular heater with a black inner surface of uniform temperature T s = 1000 K irradiates a coaxial disk. (a) Determine the radiant power from the heater which is incident on the disk, q s?1 . What...

In early January, 2020, William Wyler, CPA, a senior manager at Myers Norris Penny LLP in Regina, Saskatchewan, was assigned the task of reviewing the financial performance of Power Green Industries...

15. LO.4 Describe the external support test and the internal support test for a private foundation.

Is there a free-riding problem when several incumbents try to deter entry? Discuss.

Find the tension in the cable and the compression in the support of the sign shown inFigure. 40.0 1150 N

Find the tension in each cable inFigure 30.0 45.0 T. T. 3 475 lb

Find the tension in each cable inFigure. 50.0 T. T. 3 2200 N

Which of these is an attribute of the Common Vulnerabilities and Exposures dictionary? Countermeasures are provided freely. There is a single description for each vulnerability or exposure. It is a...

Suppose that you are predicting the number of calories consumed by adult males by the weight of adult males. Calculate the index of predictive association. a. 0.00 b. 0.44 c. 1.00 d. 0.40 e. none of...

Some ideas of things that you could post about from this week's topic: Look up the most recent interest rate decision on the RBA's website. Discuss the contents. Discuss anything about current...