The initial position, velocity, and acceleration of an object moving in simple harmonic motion are xi, vi,
Question:
(a) Show that the position and velocity of the object for all time can be written as
x (t) = x i cos wt + (vi/w) sin wt
v (t) = ─ xiw sin wt + vi cos wt
(b) If the amplitude of the motion is A, show that v2 ─ ax = vi2 ─ aixi = w2A2
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (3 reviews)
The proposed solution implies velocity and acceleration a b xtx cosaxt ...View the full answer
Answered By
Rodrigo Louie Rey
I started tutoring in college and have been doing it for about eight years now. I enjoy it because I love to help others learn and expand their understanding of the world. I thoroughly enjoy the "ah-ha" moments that my students have. Interests I enjoy hiking, kayaking, and spending time with my family and friends. Ideal Study Location I prefer to tutor in a quiet place so that my students can focus on what they are learning.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Related Video
simple harmonic motion, in physics, repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same
Students also viewed these Oscillations Mechanical Waves questions
-
The acceleration of an object moving in the gravitational field of the Earth is a = GMEr/r3 where r is the position vector directed from the center of the Earth toward the object. Choosing the origin...
-
The coordinates of an object moving in the xy plane vary with time according to the equations x= (5.00 m) sin (wt) and y= (4.00 m) (5.00 m) cos (wt), where w is a constant and t is in seconds. (a)...
-
The displacement (in meters) of an object moving in a straight line is given by s = 1 + 2t + t2/4, where is measured in seconds. (a) Find the average velocity over each time period. (i) [1, 3] (ii)...
-
The following were selected from among the transactions complete by Wild Adventures Company during December of the current year. Dec. 3. Purchased merchandise on account from Miramar Co., list price...
-
Consider the problem of placing eight queens on an (eight-by-eight) chess board. Two queens are said to attack each other if they are on the same row, column, or (not necessarily main) diagonal. a....
-
A thick-walled steel pipe (k = 60 W/m K) carrying hot water is cooled externally by a cross-flow airstream at a velocity of 20 m/s and a temperature of 25C. The inner and outer diameters of the pipe...
-
1.7 Mexico's Cada Seis Aos. Mexico was famous-or infamous-for many years for having two things every six years (cada seis aos in Spanish): a presi- dential election and a currency devaluation. This...
-
At a local university, the Student Commission on Programming and Entertainment (SCOPE) is preparing to host its first rock concert of the school year. To successfully produce this rock concert, SCOPE...
-
11. (Bond market) There are three bonds in the market as follows: 1. A bond with 4% coupon rate (paid annually), 10 years to maturity, and $1,000 face value 2. A bond with 4% plus current (short)...
-
Using the HCF Balance Sheet on page 226-227 in Table 9A-1, how could you determine the amount of debt principal that will be retired during the next fiscal year? TABLE 9A-1 Harris Memorial Hospital...
-
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...
-
A simple harmonic oscillator takes 12.0 s to undergo five complete vibrations. Find (a) The period of its motion, (b) The frequency in hertz, and (c) The angular frequency in radians per second.
-
Provide the rejection region based on a t- test statistic for the following situations: a. H0: 28 versus H: < 28 with n = 11, = .05 b. H0: 28 versus H: > 28 with n = 21, = .025 c. H0: 28...
-
A cache system has 1024 cache line with block size of 1024 bytes. It uses 22-bits TAG and 10-bits 'Ctrl' bits. What is the total size of cache memory in KB unit?
-
You hedged the sale of hogs by selling four contracts and then offsetting four futures contracts. The hedged return was $3.00/cwt. Your broker charged you a total commission of $200. What is your...
-
Due to erratic sales of its sole product-a high-capacity battery for laptop computers-PEM, Incorporated, has been experiencing financial difficulty for some time. The company's contribution format...
-
Size of cache memory is 64Kword and the size of main memory is 64M*8 bit word. Determine the word size of main memory, cache and the main memory address format. Give your answer and explain every...
-
I would like you to share your ideas about how Twitter, the company, can drive high levels of their employee engagement by using technology to improve communication. You can also relate your answers...
-
Cleanway Ltd is a public company that competes in the highly competitive market for manufactured household products. The company is dominated by Rob Bigbucks, the chairman and chief executive...
-
You are the newly appointed tax practitioner to complete Emilys tax return and have downloaded the prefill report for Emilys tax return (hint, you can read what a prefill report is here (Links to an...
-
The Bradley Co. had $185,000 in 2002 taxable income. Using the rates from Table 2.3 in the chapter, calculate the companys 2002 income taxes. Table 2.3 $ Taxable Income 50,000 50,001- 75,000 75,001-...
-
ngpf NGPF Activity Bank NEXT GEN PERSONAL FINANCE Types of Credit Spanish Version COMPARE: Auto Loans Molly is celebrating her amazing new career and wants to upgrade her junky old car for a shiny...
-
The trial balance for December 31, 2021, included the following accounts: Account Title Sales revenue Cost of goods sold Selling and administrative expense Interest expense Gain on debt securities...
-
I am unclear on how to get the flexible budget. . Osage, Inc_, manufactures and sells lamps. The company produces only when it receives orders and, therefore, has no inventories. The following...
Study smarter with the SolutionInn App