Damped Simple Harmonic Motion
PHXI14:OSCILLATIONS

364202 A particle executes \(S.H.M.\) of amplitude \(A\) along \(x\)-axis. At \(t=0\), the position of the particle is \(x=\dfrac{A}{2}\) and it moves along positive \(x\)-axis. The displacement of particle in time \(t\) is \(x=A \sin (\omega t+\delta)\), then the value \(\delta\) will be

1 \(\dfrac{\pi}{4}\)
2 \(\dfrac{\pi}{6}\)
3 \(\dfrac{\pi}{2}\)
4 \(\dfrac{\pi}{3}\)
PHXI14:OSCILLATIONS

364203 A simple harmonic motion having an amplitude \(A\) and time period \(T\) is represented by the equation :
\(y=5 \sin 2 \pi(t+4 x) m\)
Then, the values of \(A\) (in \(m\) ) and \(T\) (in sec) are :

1 \(A=5 ; T=2\)
2 \(A=10 ; T=1\)
3 \(A = 5;T = 1\;\)
4 \(A = 10;T = 2\)
PHXI14:OSCILLATIONS

364204 \(x=a \cos ^{2} \omega t\) or \(x=\dfrac{a}{2}-\dfrac{a}{2} \cos 2 \omega t\) represents
(i) Periodic motion but not simple harmonic motion if \(x\) is displacement
(ii) SHM of angular frequency \(2 \omega\)

1 Only (i) is correct
2 Only (ii) is correct
3 Both are incorrect
4 Both are correct
PHXI14:OSCILLATIONS

364205 Which one of the following equations of motion represents simple harmonic motion?

1 Acceleration \(=-k_{0} x+k_{1} x^{2}\)
2 Acceleration \(=-k(x+a)\)
3 Acceleration \(=k(x+a)\)
4 Acceleration \(=k x\)
PHXI14:OSCILLATIONS

364202 A particle executes \(S.H.M.\) of amplitude \(A\) along \(x\)-axis. At \(t=0\), the position of the particle is \(x=\dfrac{A}{2}\) and it moves along positive \(x\)-axis. The displacement of particle in time \(t\) is \(x=A \sin (\omega t+\delta)\), then the value \(\delta\) will be

1 \(\dfrac{\pi}{4}\)
2 \(\dfrac{\pi}{6}\)
3 \(\dfrac{\pi}{2}\)
4 \(\dfrac{\pi}{3}\)
PHXI14:OSCILLATIONS

364203 A simple harmonic motion having an amplitude \(A\) and time period \(T\) is represented by the equation :
\(y=5 \sin 2 \pi(t+4 x) m\)
Then, the values of \(A\) (in \(m\) ) and \(T\) (in sec) are :

1 \(A=5 ; T=2\)
2 \(A=10 ; T=1\)
3 \(A = 5;T = 1\;\)
4 \(A = 10;T = 2\)
PHXI14:OSCILLATIONS

364204 \(x=a \cos ^{2} \omega t\) or \(x=\dfrac{a}{2}-\dfrac{a}{2} \cos 2 \omega t\) represents
(i) Periodic motion but not simple harmonic motion if \(x\) is displacement
(ii) SHM of angular frequency \(2 \omega\)

1 Only (i) is correct
2 Only (ii) is correct
3 Both are incorrect
4 Both are correct
PHXI14:OSCILLATIONS

364205 Which one of the following equations of motion represents simple harmonic motion?

1 Acceleration \(=-k_{0} x+k_{1} x^{2}\)
2 Acceleration \(=-k(x+a)\)
3 Acceleration \(=k(x+a)\)
4 Acceleration \(=k x\)
PHXI14:OSCILLATIONS

364202 A particle executes \(S.H.M.\) of amplitude \(A\) along \(x\)-axis. At \(t=0\), the position of the particle is \(x=\dfrac{A}{2}\) and it moves along positive \(x\)-axis. The displacement of particle in time \(t\) is \(x=A \sin (\omega t+\delta)\), then the value \(\delta\) will be

1 \(\dfrac{\pi}{4}\)
2 \(\dfrac{\pi}{6}\)
3 \(\dfrac{\pi}{2}\)
4 \(\dfrac{\pi}{3}\)
PHXI14:OSCILLATIONS

364203 A simple harmonic motion having an amplitude \(A\) and time period \(T\) is represented by the equation :
\(y=5 \sin 2 \pi(t+4 x) m\)
Then, the values of \(A\) (in \(m\) ) and \(T\) (in sec) are :

1 \(A=5 ; T=2\)
2 \(A=10 ; T=1\)
3 \(A = 5;T = 1\;\)
4 \(A = 10;T = 2\)
PHXI14:OSCILLATIONS

364204 \(x=a \cos ^{2} \omega t\) or \(x=\dfrac{a}{2}-\dfrac{a}{2} \cos 2 \omega t\) represents
(i) Periodic motion but not simple harmonic motion if \(x\) is displacement
(ii) SHM of angular frequency \(2 \omega\)

1 Only (i) is correct
2 Only (ii) is correct
3 Both are incorrect
4 Both are correct
PHXI14:OSCILLATIONS

364205 Which one of the following equations of motion represents simple harmonic motion?

1 Acceleration \(=-k_{0} x+k_{1} x^{2}\)
2 Acceleration \(=-k(x+a)\)
3 Acceleration \(=k(x+a)\)
4 Acceleration \(=k x\)
PHXI14:OSCILLATIONS

364202 A particle executes \(S.H.M.\) of amplitude \(A\) along \(x\)-axis. At \(t=0\), the position of the particle is \(x=\dfrac{A}{2}\) and it moves along positive \(x\)-axis. The displacement of particle in time \(t\) is \(x=A \sin (\omega t+\delta)\), then the value \(\delta\) will be

1 \(\dfrac{\pi}{4}\)
2 \(\dfrac{\pi}{6}\)
3 \(\dfrac{\pi}{2}\)
4 \(\dfrac{\pi}{3}\)
PHXI14:OSCILLATIONS

364203 A simple harmonic motion having an amplitude \(A\) and time period \(T\) is represented by the equation :
\(y=5 \sin 2 \pi(t+4 x) m\)
Then, the values of \(A\) (in \(m\) ) and \(T\) (in sec) are :

1 \(A=5 ; T=2\)
2 \(A=10 ; T=1\)
3 \(A = 5;T = 1\;\)
4 \(A = 10;T = 2\)
PHXI14:OSCILLATIONS

364204 \(x=a \cos ^{2} \omega t\) or \(x=\dfrac{a}{2}-\dfrac{a}{2} \cos 2 \omega t\) represents
(i) Periodic motion but not simple harmonic motion if \(x\) is displacement
(ii) SHM of angular frequency \(2 \omega\)

1 Only (i) is correct
2 Only (ii) is correct
3 Both are incorrect
4 Both are correct
PHXI14:OSCILLATIONS

364205 Which one of the following equations of motion represents simple harmonic motion?

1 Acceleration \(=-k_{0} x+k_{1} x^{2}\)
2 Acceleration \(=-k(x+a)\)
3 Acceleration \(=k(x+a)\)
4 Acceleration \(=k x\)