Homework 11 Problems вЂ“ Simple Harmonic Motion 1. [10 points] A grandfather clock depends on the period of a pendulum to keep correct time. Suppose such a clock is calibrated correctly and then the temperature of the room in which it resides increases. a. Does the clock run slow, fast, or correctly? [Hint: A material expands when its temperature increases.] b. How could we adjust the length of the pendulum to correct the time? 2. [10 points] A block of mass is attached to a spring of force constant that lies on a horizontal surface as shown below. The block is pulled to a position to the right of the equilibrium and released from rest. a. Find the work required to stretch the spring. b. Find the speed the block as it passes through equilibrium. 3. [10 points] A 2.00-kg object on a frictionless track is attached to the end of a horizontal spring whose force constant is 5.00 N/m. The object is displaced 3.00 m to the right from its equilibrium position, initiating simple harmonic motion. a. What is the force (magnitude and direction) acting on the object 3.50 s after it is released. b. How many times does the object oscillate in 3.50 s? 4. [10 points] The position of a 0.30-kg object attached to a spring is described by ( ) ( ) a. Find the amplitude of the motion and the spring constant b. Find the position of the object and the force exerted on the object at c. Find the objectвЂ™s speed and acceleration at d. Determine the kinetic energy, potential energy, and total energy at 5. [10 points] A 5.00-g bullet moving with an initial speed of 400 m/s is fired into and passes through a 1.00-kg block, as shown below. The block, initially at rest on a frictionless horizontal surface, is connected to a spring with a spring constant of 900 N/m. If the block moves 5.00 cm to the right after impact, a. Find the speed at which the bullet emerges from the block and b. Find the mechanical energy lost in the collision. Bonus: [6 points] A large block P executes simple harmonic motion as it slides across a frictionless surface with a frequency . Block B rests on it, as shown below, and the coefficient of static friction between the two is . What maximum amplitude of oscillation can the system have if block B is not to slip?