Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 41 Hw: Chapter 15 problems and exercises

Simple harmonic oscillator

Examples Lots of stuff Vibrates or Oscillates: –Radio Waves –Guitar Strings –Atoms –Clocks, etc…

Why do we care? Lots of engineering problems are oscillation problems –Buildings vibrating in the wind –Motors vibrating when running –Solids vibrating when struck –Earthquakes

Resonance

The forces No force Force in –x direction Force in +x direction

More Detail Time

Some Terms Amplitude: Max distance Period: Time it takes to get back to here

A block with mass m is attached to the end of a spring, with spring constant k. The spring is stretched a distance L and let go at t=0 Find the position of the mass at all times Where does the maximum speed occur? What is the maximum speed?

If the block is pulled a distance x 1 to the right and released from rest, how long will it take the block to return to its equilibrium position? How does this time change if the displacement is increased from x 1 to 2x 1 ? How fast will the block be moving at its equilibrium position for the x 1 displacement?

A bullet of mass m is fired with velocity of magnitude into a block of mass M. The block is connected to a spring constant k and rests on a frictionless surface. Find the velocity of the block as a function of time. (Assume the bullet comes to rest infinitely quickly in the block, i.e. during the collision the spring doesn’t get compressed.)

Simple pendulum How long does it take to return to the equilibrium?

Have a great day! Hw: Chapter 18 problems and exercises