Problem is given below full points to whoever answers and explains their work. P

Question

Problem is given below full points to whoever answers and explains their work. Please don't give me just the answer as I will need to know how to work out the problem. Thank you.

A 2.00 kg frictionless block is attached to a horizontal spring as shown. Spring constant k = 200.00 N/m. At t = 0: the position x = 0.225 m: and the velocity is 4.25 m/s toward the right in the positive x direction. Position x as a function of t is: x = A*cos(omega t + theta) : where A is the amplitude of motion and co is the angular frequency discussed Chapter 11 and the notes. Theta is called the phase constant that will be addressed for extra credit below. Use conservation of energy to compute amplitude A. How much farther from the point shown will the block move before it momentarily comes to rest before turning around? What is the period T of the motion? If the mass of this problem was doubled to 4.00 kg: how would your answer to part (c ) change? EXTRA CREDIT: Use your trigonometry background to find phase constant theta.

Explanation / Answer

a)      0.5*m*v^2 + 0.5*kx^2 = 0.5*k*A^2

=>0.5*2*4.25^2 + 0.5*200*0.225^2 = 0.5*200*A^2

=>A = 0.481 m

b)      Ans = A-x = 0.481

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