Some Systems Executing Simple Harmonic Motion
PHXI14:OSCILLATIONS

364364 A block of mass \(m\) is tied to one end of a spring which passes over a smooth fixed pulley \(A\) and under a light smooth movable pulley \(B\). The other end of the string is attached to the lower end of a spring of spring constant \(K_{2}\). Find the period of small oscillation of mass \(m\) about its equilibrium position.
(Take \(m=\pi^{2} {~kg}\), \(K_{2}=4 K_{1}\) and\({K_1} = 17{\rm{ }}N/m\).
supporting img

1 \(1\,s\)
2 \(3\,s\)
3 \(7\,s\)
4 \(9\,s\)
PHXI14:OSCILLATIONS

364365 If each spring in figure has force constant of \({10 \dfrac{{N}}{{m}}}\), and attach mass is \(10\,kg\), then find the frequency of oscillation.
supporting img

1 \({\pi H z}\)
2 \({\dfrac{1}{\pi} H z}\)
3 \(2\,Hz\)
4 \({\dfrac{2}{\pi} {Hz}}\)
PHXI14:OSCILLATIONS

364366 A uniform stick of mass \(M\) and length \(L\) is pivoted at its centre. Its ends are tied to two springs each of force constant \(K\). In the position shown figure, the strings are in their natural length. When the string is displaced through a small angle \(\theta\) and released. The stick:
supporting img

1 Executes periodic motion which is not simple harmonic
2 Executes non-periodic motion
3 Executes S.H.M. of frequency \(\dfrac{1}{2 \pi} \sqrt{\dfrac{6 K}{M}}\)
4 Executes S.H.M. of frequency \(\dfrac{1}{2 \pi} \sqrt{\dfrac{K}{2 M}}\)
PHXI14:OSCILLATIONS

364367 Two blocks each of mass \(m = 1\;kg\) are connected to the spring of spring constant \(k = 2\) units (as in fig.) If the blocks are displaced slightly in opposite directions and released, they will execute SHM. What is the time period of oscillation ?
supporting img

1 \(3.14\,s\)
2 \(1.27\,s\)
3 \(6.13\,s\)
4 \(4.25\,s\)
PHXI14:OSCILLATIONS

364364 A block of mass \(m\) is tied to one end of a spring which passes over a smooth fixed pulley \(A\) and under a light smooth movable pulley \(B\). The other end of the string is attached to the lower end of a spring of spring constant \(K_{2}\). Find the period of small oscillation of mass \(m\) about its equilibrium position.
(Take \(m=\pi^{2} {~kg}\), \(K_{2}=4 K_{1}\) and\({K_1} = 17{\rm{ }}N/m\).
supporting img

1 \(1\,s\)
2 \(3\,s\)
3 \(7\,s\)
4 \(9\,s\)
PHXI14:OSCILLATIONS

364365 If each spring in figure has force constant of \({10 \dfrac{{N}}{{m}}}\), and attach mass is \(10\,kg\), then find the frequency of oscillation.
supporting img

1 \({\pi H z}\)
2 \({\dfrac{1}{\pi} H z}\)
3 \(2\,Hz\)
4 \({\dfrac{2}{\pi} {Hz}}\)
PHXI14:OSCILLATIONS

364366 A uniform stick of mass \(M\) and length \(L\) is pivoted at its centre. Its ends are tied to two springs each of force constant \(K\). In the position shown figure, the strings are in their natural length. When the string is displaced through a small angle \(\theta\) and released. The stick:
supporting img

1 Executes periodic motion which is not simple harmonic
2 Executes non-periodic motion
3 Executes S.H.M. of frequency \(\dfrac{1}{2 \pi} \sqrt{\dfrac{6 K}{M}}\)
4 Executes S.H.M. of frequency \(\dfrac{1}{2 \pi} \sqrt{\dfrac{K}{2 M}}\)
PHXI14:OSCILLATIONS

364367 Two blocks each of mass \(m = 1\;kg\) are connected to the spring of spring constant \(k = 2\) units (as in fig.) If the blocks are displaced slightly in opposite directions and released, they will execute SHM. What is the time period of oscillation ?
supporting img

1 \(3.14\,s\)
2 \(1.27\,s\)
3 \(6.13\,s\)
4 \(4.25\,s\)
PHXI14:OSCILLATIONS

364364 A block of mass \(m\) is tied to one end of a spring which passes over a smooth fixed pulley \(A\) and under a light smooth movable pulley \(B\). The other end of the string is attached to the lower end of a spring of spring constant \(K_{2}\). Find the period of small oscillation of mass \(m\) about its equilibrium position.
(Take \(m=\pi^{2} {~kg}\), \(K_{2}=4 K_{1}\) and\({K_1} = 17{\rm{ }}N/m\).
supporting img

1 \(1\,s\)
2 \(3\,s\)
3 \(7\,s\)
4 \(9\,s\)
PHXI14:OSCILLATIONS

364365 If each spring in figure has force constant of \({10 \dfrac{{N}}{{m}}}\), and attach mass is \(10\,kg\), then find the frequency of oscillation.
supporting img

1 \({\pi H z}\)
2 \({\dfrac{1}{\pi} H z}\)
3 \(2\,Hz\)
4 \({\dfrac{2}{\pi} {Hz}}\)
PHXI14:OSCILLATIONS

364366 A uniform stick of mass \(M\) and length \(L\) is pivoted at its centre. Its ends are tied to two springs each of force constant \(K\). In the position shown figure, the strings are in their natural length. When the string is displaced through a small angle \(\theta\) and released. The stick:
supporting img

1 Executes periodic motion which is not simple harmonic
2 Executes non-periodic motion
3 Executes S.H.M. of frequency \(\dfrac{1}{2 \pi} \sqrt{\dfrac{6 K}{M}}\)
4 Executes S.H.M. of frequency \(\dfrac{1}{2 \pi} \sqrt{\dfrac{K}{2 M}}\)
PHXI14:OSCILLATIONS

364367 Two blocks each of mass \(m = 1\;kg\) are connected to the spring of spring constant \(k = 2\) units (as in fig.) If the blocks are displaced slightly in opposite directions and released, they will execute SHM. What is the time period of oscillation ?
supporting img

1 \(3.14\,s\)
2 \(1.27\,s\)
3 \(6.13\,s\)
4 \(4.25\,s\)
PHXI14:OSCILLATIONS

364364 A block of mass \(m\) is tied to one end of a spring which passes over a smooth fixed pulley \(A\) and under a light smooth movable pulley \(B\). The other end of the string is attached to the lower end of a spring of spring constant \(K_{2}\). Find the period of small oscillation of mass \(m\) about its equilibrium position.
(Take \(m=\pi^{2} {~kg}\), \(K_{2}=4 K_{1}\) and\({K_1} = 17{\rm{ }}N/m\).
supporting img

1 \(1\,s\)
2 \(3\,s\)
3 \(7\,s\)
4 \(9\,s\)
PHXI14:OSCILLATIONS

364365 If each spring in figure has force constant of \({10 \dfrac{{N}}{{m}}}\), and attach mass is \(10\,kg\), then find the frequency of oscillation.
supporting img

1 \({\pi H z}\)
2 \({\dfrac{1}{\pi} H z}\)
3 \(2\,Hz\)
4 \({\dfrac{2}{\pi} {Hz}}\)
PHXI14:OSCILLATIONS

364366 A uniform stick of mass \(M\) and length \(L\) is pivoted at its centre. Its ends are tied to two springs each of force constant \(K\). In the position shown figure, the strings are in their natural length. When the string is displaced through a small angle \(\theta\) and released. The stick:
supporting img

1 Executes periodic motion which is not simple harmonic
2 Executes non-periodic motion
3 Executes S.H.M. of frequency \(\dfrac{1}{2 \pi} \sqrt{\dfrac{6 K}{M}}\)
4 Executes S.H.M. of frequency \(\dfrac{1}{2 \pi} \sqrt{\dfrac{K}{2 M}}\)
PHXI14:OSCILLATIONS

364367 Two blocks each of mass \(m = 1\;kg\) are connected to the spring of spring constant \(k = 2\) units (as in fig.) If the blocks are displaced slightly in opposite directions and released, they will execute SHM. What is the time period of oscillation ?
supporting img

1 \(3.14\,s\)
2 \(1.27\,s\)
3 \(6.13\,s\)
4 \(4.25\,s\)