Question

Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without friction as in the figure. The bead is connected to an ideal spring of spring constant k, and the other end of the spring is connected to a fixed point at a perpendicular distance d from the wire. Unstretched length of the spring is very small, and can be taken to be zero. a) What is the period of oscillations of the bead around its equilibrium position? b) What is the amplitude of the simple harmonic motion if we give the bead an initial velocity of vo at its equilibrium position? c) Find the position of the bead as a function of time, x(t), for the case in part b.

Answer 1

Solution :- TN t=0 VVO (b) Amplitude of Oscillation :- In this case, it is not a function of time but it depends on initial velocity and position => we will use equation of Energy, Eis Et 1 ŁKA Į KM²+ 2 muz :: t=0, x=0 - Lso, kako => + KA² + mv2 (9) To period of oscillation can be given by T= = = 2ml [:w=57] Scanned with CamScanner

'C) X(t)= A coswt *(t) = # me vo cosur TAH (period) T -A + Scanned With CamScanner