Phys 142 - Tutorial HW 1

Tutorial Homework: Simple harmonic motion Name: _J& /07 & 77" , Section 1. A simple pendulum consists of a particle of mass m suspended by a long, massless wire of length L. (Note: Ne glect all frictional effects.) ndulum bob u;rreqpnndmg to a moment when the bob Draw a free-body diagram for the pe ! he right of) equilibrium. a \n angular displacement g away from (eg.,tot is located A AN - b. Determine an expression (in terms of m, g, and ¢) for the component of the net force on the bob that points tangent to the path of the bob. o Is this (tangential) component of the net force on the bob characteristic of a restoring force? Explain how you can tell. ; g / hd (ectores e an i the bCcryye Vicrt UVl S~ « Will this (tangential) component of the net force necessarily result in simple harmonic motion? Explain how you can tell. \/ [ 1 £ C J - Hm /r ¢ { he ¢. Now assume that the pendulum bob undergoes small (angular) displacements from equilibrium. That is, assume that for all values of angular displacement ¢ from equilibrium, sin ¢=tan ¢= ¢ (¢din radians) i. Simplify your expression for the tangential component of the net force (from part b), and use Newton's Second Law to write down the resulting differential equation of motion for the angular position ¢(t) of the pendulum bob as a function of time. G A cos ((wt :[’) ©2013 Physics Department, Grand Valley State University, Allendale, M1, Edited at Cal Poly, 2020.