Reference no: EM131321160
To understand the application of the general harmonic equation to finding the acceleration of a spring oscillator as a function of time. One end of a spring with spring constant k is attached to the wall. The other end is attached to a block of mass m. The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be x = 0. The length of the relaxed spring is L, shown in the Fig. 3.
The block is slowly pulled from its equilibrium position to some position xinit > 0 along the x axis. At time t = 0 , the block is released with zero initial velocity. The goal of this problem is to determine the acceleration of the block a(t) as a function of time in terms of
Fig. 3: Figure for problem 6
k, m, and xinit. It is known that a general solution for the position of a harmonic oscillator is x(t) = C cos(ωt) + S sin(ωt), where C, S, and ω are constants (Fig. 4). Your task, therefore, is to determine the values of C, S, and ω in terms of k, m,and xinit and then use the connection between x(t) and a(t) to find the acceleration.
Fig. 4: Figure for problem 6
(a) Combine Newton's 2nd law and Hooke's law for a spring to find the acceleration of the block a(t) as a function of time. Express answer in terms of k, m, and x(t).
(b) Using the fact that acceleration is the second derivative of position, find the acceler- ation of the block a(t) as a function of time. Express your answer in terms of ω and x(t).
(c) Using your solutions from (a) and (b) find the angular frequency ω. Express your answer in terms of k and m.
Is now the time to invest in long term bonds
: Define the agency problem, and discuss how to resolve it from the perspective of a stockholder. Is now the time to invest in long term bonds? If not, why not? Has Starbucks breached its fiduciary duty to shareholders by investing its profits in free ..
|
Describe the most common descriptive statistics
: What is the difference between descriptive and inferential statistics?
|
Calculate the post tax mortgage cost for year
: A family currently live in an apartment whose monthly rent is $950. They are thinking of buying a house which would cost $220,000. They plan to live in this house for 5 years and sell it at the end of the 5th year. Calculate the Post tax Mortgage Cos..
|
Financial ratio is one financial value
: A ratio is one value expressed to another. A financial ratio is one financial value or measurement expressed to another. There are about 20 financial ratios commonly used to assess one company's performance compared to another company in the same ind..
|
Application of the general harmonic equation
: To understand the application of the general harmonic equation to finding the acceleration of a spring oscillator as a function of time. One end of a spring with spring constant k is attached to the wall. The other end is attached to a block of ma..
|
Risks and costs to the employees
: Starbucks partnered with Arizona State University (ASU) to offer a custom online undergraduate degree program for all Starbucks employees, at an affordable price. Is this a truly free college program, or are there risks and costs to the employees? If..
|
Who can treat others and be treated rightly or wrongly
: Relativism and absolutism seem like polar opposites. One states there are many ways one can become good, and another states that there is really only one way to become good. However, both can adopt some form of egoism. Use the works of philos..
|
Demonstrate the fast diffusivity of fe in si
: Demonstrate the fast diffusivity of Fe in Si by extrapolating the high-temperature diffusivity of Fe in Si (given Figure) to room temperature.
|
Calculate the oscillation frequency
: Calculate the oscillation frequency f of the H2 molecule. Use meff = m/2 as the "effective mass" of the system, where m in the mass of a hydrogen atom. Take the mass of a hydrogen atom as 1.008 u, where 1 u = 1.6611027 kg. Express your answer in h..
|