Question: could you please help me with these two questions full...
Could you please help me with these two questions. Full solution big like and comment.
3. Dr. Beta is demonstrating simple harmonic motion to his class using a 2.00 kg mass on a spring with a force constant of k = 40.0 N m−1 . He calculates the period expected; then he asks a volunteer to displace the mass by 0.20 m from its equilibrium position and release it so that they can check the period experimentally. The volunteer decides to try to disrupt the experiment by releasing the mass with a push, such that it has 1.00 J of kinetic energy when released (at the requested position 0.20 m from equilibrium).
(a) The mass oscillates with an amplitude greater than the 0.20 m amplitude Dr.Beta was expecting, calculate the amplitude observed. Explain your reasoning.(how do calculate the amplitude) (b) Calculate the period of the oscillation observed.
(c) This period matches the one calculated by Dr. Beta, explain why the attempt to disrupt the experiment failed.
4. A 1.20 m long cylindrical rod is used to make a pendulum. The rod is suspended from one of its ends and a 8.00 kg point mass is attached to the other end. The angular displacement of the pendulum as a function of time is given by θ(t) = A cos(ω0t + φ0)
(a) Derive the period of the pendulum’s small amplitude oscillation, using the approximation of a massless rod.
(b) If the rod actually has a mass of 2.5 kg, recalculate the period of oscillation. [Note] The moment of inertia for a rod rotating about one of its ends, is given by I = 1 3mL2 , where m is the rod’s mass and L is its length.