A glider is oscillating in SHM on an air track with an amplitude A1 You slow it

Question

A glider is oscillating in SHM on an air track with an amplitude A1 You slow it so that its amplitude is halved. (a) What happens to its period? 2 What happens to its frequency? What happens to its angular frequency? 01 (b) What happens to its total mechanical energy? 2 (c) What happens to its maximum speed? max 2 = Vmax 1 (d) what happens to its speed at x =-A1/2? v1 (x = ±A1/2) (e) what happens to its potential energy at x =-A1/2? U2(x = ±A1/2) = Uy(x = ±A1/2) what happens to its kinetic energy at x = ±A/2?

Explanation / Answer

Period ,frequency and angular frequency are independent of amplitude .Therefore

a)

T2=(1)T1

f2=(1)f1

W2=(1)W1

b)

Total energy

E=(1/2)KA2

=>E2/E1=(A2/A1)2=(1/2)2

E2=(1/4)E1

c)

Maximum speed

Vmax =AW

=>Vmax2/Vmax1 =A2/A1 =1/2

Vmax2 =(1/2)Vmax1

d)

Vx=sqrt(K/m)*sqrt(A2-x2)

V1(x=A/2)=sqrt(K/m)*sqrt(A12-A12/4)=[sqrt(3)/2]A1*sqrt(K/m)

V2(x=A/2)=sqrt(K/m)*sqrt(A12/4-A12/4)=0

=>V2(x=A/2)=(0)V1(x=A/2)

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