Question

Activity 2. Finding the spring constant of a spring: DYNAMIC METHOD A spring of length L is connected to a support. A small mass m is connected to the spring pulling on this mass, the spring is stretched down a distance A from its equilibrium position. When the mass is let go, it starts oscillating up and down. The position of the mass changes as shown in the graph below. a) What type of motion does the graph describe? b) On the graph, indicate the amplitude and period of motion for the oscillating mass. C) The mathematical expression for the position of the oscillating mass as a function of time is in general written as (fill in the blanks): X= sin( sin(. +0) (In PHY1210 lecture, we use a cosine function. Sine and cosine functions have the similar shape and amplitude, but they are shifted horizontally relative to each other, the shift is indicated by the O. Here the ois not important.) d) How is the angular frequency to connected to the mass and the spring constant of the spring? Write the mathematical equation connecting these physical quantities. This is equation 1. w= e) From equation 1, find the spring constant k. This is equation 2. 1) Sketch a graph of was a function of 1/mass. What does the slope of this graph represent?

Answer 1

The solution is given below.

a The Graph describes a 'simple Harmonic Motion. 1x tat- - A 7/2 37 2/2 T 77 2T 2T - - - --- a amplitude of motion Ty period of motion

x= asin (wt+8) at amplitude wy angular frequeney & initial phase t time, of Relation and constant- angular mass is frequency with spring com 0 ky spring Constant mm moss Squasing both sides of equation ③ we get os, ka mw2 - Equation ② gives in terms of the mass expression of and angular spring constant frequency. & whs I [ from equation ] or we constant & , constant ak = spring Constant. so we ws m plot gives a straight line and slope of this straight line gives the value of spoing constant Slope =k W2

Thank you