A particle moving with SHM has speeds 3cm/s and 4cm/s at displacements 8cm and 6cm respectively,from the equilibrium position Find - Physics - Oscillations

Question

A particle moving with SHM has speeds 3cm/s and 4cm/s at
displacements 8cm and 6cm respectively,from the equilibrium
position Find - (1) Time period of the oscillations
(2)​Amplitude of the oscillations

Piyush Sindhi · Accepted Answer

Sol: Velocity of a particle during SHM is given by following
formula:
v = ωA2-x2where:A = Amplitudex = displacement from mean position(1)
 As per given that: v = 3 cmsec at x = 8 cmso3 = ωA2-823 = ωA2-64                         
(1)(2)
 As per given thatv = 4 cmsec at x = 6 cmso4 = ωA2-624 = ωA2-36                         
(2)dividing eq 
(2) by (1)169 = A2-36A2-6416A2-16×64 = 9A2-36×97A2 = 1024-324 = 700A = ±10So the value of amplitude will be:A = 10 cm                                        
(3)now putting value of eq 
(3) in 
(1)3 = ω102-643 = ω100-643 = ω×6ω = 12so the time period will be given as:T = 2πωT = 2π12T = 4π sec

A particle moving with SHM has speeds 3cm/s and 4cm/s at displacements 8cm and 6cm respectively,from the equilibrium position.Find - (1) Time period of the oscillations (2)​Amplitude of the oscillations

A particle moving with SHM has speeds 3cm/s and 4cm/s at displacements 8cm and 6cm respectively,from the equilibrium position.Find - (1) Time period of the oscillations (2)Amplitude of the oscillations