Two simple harmonic motions of angular frequency 100 rad s−1100 rad s−1 and 1000 rad s−11000 rad s−1 have the same displacement amplitude. The ratio of their maximum acceleration will be:
1. 1:101:10
2. 1:1021:102
3. 1:1031:103
4. 1:1041:104
A point performs simple harmonic oscillation of period T and the equation of motion is given by x= a sin (ωt +π/6)(ωt +π/6).After the elapse of what fraction of the time period the velocity of the point will be equal to half to its maximum velocity?
1. T8T8
2. T6T6
3. T3 T3
4 T 12T 12
The angular velocities of three bodies in simple harmonic motion are ω1,ω2,ω3ω1,ω2,ω3 with their respective amplitudes as A1,A2,A3A1,A2,A3. If all the three bodies have same mass and maximum velocity, then
1. A1ω1=A2ω2=A3ω3A1ω1=A2ω2=A3ω3
2. A1ω12=A2ω22=A3A32A1ω12=A2ω22=A3A32
3. A12ω1=A22ω2=A32ω3A12ω1=A22ω2=A32ω3
4. A12ω12=A22ω22=A2A12ω12=A22ω22=A2
The amplitude of a particle executing SHM is 4 cm. At the mean position the speed of the particle is 16 cm/sec. The distance of the particle from the mean position at which the speed of the particle becomes 8√3cm/sec8√3cm/sec will be
1. 2√3cm2√3cm
2. √3cm√3cm
3. 1 cm
4. 2 cm
The maximum velocity of a simple harmonic motion represented by y=3 sin (100t+π6)y=3 sin (100t+π6) is given by
1. 300
2. 3π63π6
3. 100
4. π6π6
The displacement equation of a particle is x=3sin 2t+4cos 2t x=3sin 2t+4cos 2t The amplitude and maximum velocity will be respectively
1. 5, 10
2. 3, 2
3. 4, 2
4. 3, 4
The instantaneous displacement of a simple pendulum oscillator is given by x=A cos (ωt+π4)x=A cos (ωt+π4) . Its speed will be maximum at time
1. π4ωπ4ω
2. π2ωπ2ω
3. πωπω
4. 2πω2πω