Some Systems Executing Simple Harmonic Motion
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PHXI14:OSCILLATIONS

364385 An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is \(15\;cm/\sec \) and the time \(\frac{\pi }{5}\,\sec \), find its amplitude

1 2.0
2 3.0
3 1.0
4 1.5
PHXI14:OSCILLATIONS

364386 Two identical particles each of mass \(m\) are interconnected by a light spring of stiffness \(k\), the time period for small oscillation is equal to:
supporting img

1 \(\dfrac{\pi}{2} \sqrt{\dfrac{m}{k}}\)
2 \(2 \pi \sqrt{\dfrac{m}{k}}\)
3 \(\pi \sqrt{\dfrac{2 m}{k}}\)
4 \(\pi \sqrt{\dfrac{m}{2 k}}\)
PHXI14:OSCILLATIONS

364387 A mass \({M}\) is suspended with a light spring. An additional mass \({m}\) added displaces the spring further by a distance \({x}\) Now, the combined mass will oscillate on the spring with period

1 \({T=2 \pi \sqrt{\dfrac{m g}{x(M+m)}}}\)
2 \({T=2 \pi \sqrt{\dfrac{(M+m) x}{m g}}}\)
3 \({T=\dfrac{\pi}{2} \sqrt{\dfrac{m g}{x(M+m)}}}\)
4 \({T=2 \pi \sqrt{\dfrac{M+m}{m g x}}}\)
PHXI14:OSCILLATIONS

364388 A block of mass \(M\) is suspended from a light spring of force constant \(k\). Another mass \(m\) moving upwards with velocity \(v\) shifts the mass \(M\) and gets embeded in it. What will be the amplitude of the combined mass?

1 \(\dfrac{m v}{\sqrt{(M-m) k}}\)
2 \(\dfrac{m v}{k \sqrt{(M-m)}}\)
3 \(\dfrac{m v}{\sqrt{(M+m) k}}\)
4 \(\dfrac{m v}{k \sqrt{(M+m)}}\)
PHXI14:OSCILLATIONS

364389 The masses \(m_{1}\) and \(m_{2}\) are suspended together by a massless spring of constant \(k\). When the masses are in equilibrium, \(m_{1}\) is removed without disturbing the system; the amplitude of vibration is -

1 \(m_{2} g / k\)
2 \(m_{1} g / k\)
3 \(\dfrac{\left(m_{2}-m_{1}\right) g}{k}\)
4 \(\dfrac{\left(m_{1}+m_{2}\right) g}{k}\)
NEET DIGITAL LIBRARY
PHXI14:OSCILLATIONS

364385 An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is \(15\;cm/\sec \) and the time \(\frac{\pi }{5}\,\sec \), find its amplitude

1 2.0
2 3.0
3 1.0
4 1.5
PHXI14:OSCILLATIONS

364386 Two identical particles each of mass \(m\) are interconnected by a light spring of stiffness \(k\), the time period for small oscillation is equal to:
supporting img

1 \(\dfrac{\pi}{2} \sqrt{\dfrac{m}{k}}\)
2 \(2 \pi \sqrt{\dfrac{m}{k}}\)
3 \(\pi \sqrt{\dfrac{2 m}{k}}\)
4 \(\pi \sqrt{\dfrac{m}{2 k}}\)
PHXI14:OSCILLATIONS

364387 A mass \({M}\) is suspended with a light spring. An additional mass \({m}\) added displaces the spring further by a distance \({x}\) Now, the combined mass will oscillate on the spring with period

1 \({T=2 \pi \sqrt{\dfrac{m g}{x(M+m)}}}\)
2 \({T=2 \pi \sqrt{\dfrac{(M+m) x}{m g}}}\)
3 \({T=\dfrac{\pi}{2} \sqrt{\dfrac{m g}{x(M+m)}}}\)
4 \({T=2 \pi \sqrt{\dfrac{M+m}{m g x}}}\)
PHXI14:OSCILLATIONS

364388 A block of mass \(M\) is suspended from a light spring of force constant \(k\). Another mass \(m\) moving upwards with velocity \(v\) shifts the mass \(M\) and gets embeded in it. What will be the amplitude of the combined mass?

1 \(\dfrac{m v}{\sqrt{(M-m) k}}\)
2 \(\dfrac{m v}{k \sqrt{(M-m)}}\)
3 \(\dfrac{m v}{\sqrt{(M+m) k}}\)
4 \(\dfrac{m v}{k \sqrt{(M+m)}}\)
PHXI14:OSCILLATIONS

364389 The masses \(m_{1}\) and \(m_{2}\) are suspended together by a massless spring of constant \(k\). When the masses are in equilibrium, \(m_{1}\) is removed without disturbing the system; the amplitude of vibration is -

1 \(m_{2} g / k\)
2 \(m_{1} g / k\)
3 \(\dfrac{\left(m_{2}-m_{1}\right) g}{k}\)
4 \(\dfrac{\left(m_{1}+m_{2}\right) g}{k}\)
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PHXI14:OSCILLATIONS

364385 An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is \(15\;cm/\sec \) and the time \(\frac{\pi }{5}\,\sec \), find its amplitude

1 2.0
2 3.0
3 1.0
4 1.5
PHXI14:OSCILLATIONS

364386 Two identical particles each of mass \(m\) are interconnected by a light spring of stiffness \(k\), the time period for small oscillation is equal to:
supporting img

1 \(\dfrac{\pi}{2} \sqrt{\dfrac{m}{k}}\)
2 \(2 \pi \sqrt{\dfrac{m}{k}}\)
3 \(\pi \sqrt{\dfrac{2 m}{k}}\)
4 \(\pi \sqrt{\dfrac{m}{2 k}}\)
PHXI14:OSCILLATIONS

364387 A mass \({M}\) is suspended with a light spring. An additional mass \({m}\) added displaces the spring further by a distance \({x}\) Now, the combined mass will oscillate on the spring with period

1 \({T=2 \pi \sqrt{\dfrac{m g}{x(M+m)}}}\)
2 \({T=2 \pi \sqrt{\dfrac{(M+m) x}{m g}}}\)
3 \({T=\dfrac{\pi}{2} \sqrt{\dfrac{m g}{x(M+m)}}}\)
4 \({T=2 \pi \sqrt{\dfrac{M+m}{m g x}}}\)
PHXI14:OSCILLATIONS

364388 A block of mass \(M\) is suspended from a light spring of force constant \(k\). Another mass \(m\) moving upwards with velocity \(v\) shifts the mass \(M\) and gets embeded in it. What will be the amplitude of the combined mass?

1 \(\dfrac{m v}{\sqrt{(M-m) k}}\)
2 \(\dfrac{m v}{k \sqrt{(M-m)}}\)
3 \(\dfrac{m v}{\sqrt{(M+m) k}}\)
4 \(\dfrac{m v}{k \sqrt{(M+m)}}\)
PHXI14:OSCILLATIONS

364389 The masses \(m_{1}\) and \(m_{2}\) are suspended together by a massless spring of constant \(k\). When the masses are in equilibrium, \(m_{1}\) is removed without disturbing the system; the amplitude of vibration is -

1 \(m_{2} g / k\)
2 \(m_{1} g / k\)
3 \(\dfrac{\left(m_{2}-m_{1}\right) g}{k}\)
4 \(\dfrac{\left(m_{1}+m_{2}\right) g}{k}\)
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PHXI14:OSCILLATIONS

364385 An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is \(15\;cm/\sec \) and the time \(\frac{\pi }{5}\,\sec \), find its amplitude

1 2.0
2 3.0
3 1.0
4 1.5
PHXI14:OSCILLATIONS

364386 Two identical particles each of mass \(m\) are interconnected by a light spring of stiffness \(k\), the time period for small oscillation is equal to:
supporting img

1 \(\dfrac{\pi}{2} \sqrt{\dfrac{m}{k}}\)
2 \(2 \pi \sqrt{\dfrac{m}{k}}\)
3 \(\pi \sqrt{\dfrac{2 m}{k}}\)
4 \(\pi \sqrt{\dfrac{m}{2 k}}\)
PHXI14:OSCILLATIONS

364387 A mass \({M}\) is suspended with a light spring. An additional mass \({m}\) added displaces the spring further by a distance \({x}\) Now, the combined mass will oscillate on the spring with period

1 \({T=2 \pi \sqrt{\dfrac{m g}{x(M+m)}}}\)
2 \({T=2 \pi \sqrt{\dfrac{(M+m) x}{m g}}}\)
3 \({T=\dfrac{\pi}{2} \sqrt{\dfrac{m g}{x(M+m)}}}\)
4 \({T=2 \pi \sqrt{\dfrac{M+m}{m g x}}}\)
PHXI14:OSCILLATIONS

364388 A block of mass \(M\) is suspended from a light spring of force constant \(k\). Another mass \(m\) moving upwards with velocity \(v\) shifts the mass \(M\) and gets embeded in it. What will be the amplitude of the combined mass?

1 \(\dfrac{m v}{\sqrt{(M-m) k}}\)
2 \(\dfrac{m v}{k \sqrt{(M-m)}}\)
3 \(\dfrac{m v}{\sqrt{(M+m) k}}\)
4 \(\dfrac{m v}{k \sqrt{(M+m)}}\)
PHXI14:OSCILLATIONS

364389 The masses \(m_{1}\) and \(m_{2}\) are suspended together by a massless spring of constant \(k\). When the masses are in equilibrium, \(m_{1}\) is removed without disturbing the system; the amplitude of vibration is -

1 \(m_{2} g / k\)
2 \(m_{1} g / k\)
3 \(\dfrac{\left(m_{2}-m_{1}\right) g}{k}\)
4 \(\dfrac{\left(m_{1}+m_{2}\right) g}{k}\)
NEET DIGITAL LIBRARY
PHXI14:OSCILLATIONS

364385 An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is \(15\;cm/\sec \) and the time \(\frac{\pi }{5}\,\sec \), find its amplitude

1 2.0
2 3.0
3 1.0
4 1.5
PHXI14:OSCILLATIONS

364386 Two identical particles each of mass \(m\) are interconnected by a light spring of stiffness \(k\), the time period for small oscillation is equal to:
supporting img

1 \(\dfrac{\pi}{2} \sqrt{\dfrac{m}{k}}\)
2 \(2 \pi \sqrt{\dfrac{m}{k}}\)
3 \(\pi \sqrt{\dfrac{2 m}{k}}\)
4 \(\pi \sqrt{\dfrac{m}{2 k}}\)
PHXI14:OSCILLATIONS

364387 A mass \({M}\) is suspended with a light spring. An additional mass \({m}\) added displaces the spring further by a distance \({x}\) Now, the combined mass will oscillate on the spring with period

1 \({T=2 \pi \sqrt{\dfrac{m g}{x(M+m)}}}\)
2 \({T=2 \pi \sqrt{\dfrac{(M+m) x}{m g}}}\)
3 \({T=\dfrac{\pi}{2} \sqrt{\dfrac{m g}{x(M+m)}}}\)
4 \({T=2 \pi \sqrt{\dfrac{M+m}{m g x}}}\)
PHXI14:OSCILLATIONS

364388 A block of mass \(M\) is suspended from a light spring of force constant \(k\). Another mass \(m\) moving upwards with velocity \(v\) shifts the mass \(M\) and gets embeded in it. What will be the amplitude of the combined mass?

1 \(\dfrac{m v}{\sqrt{(M-m) k}}\)
2 \(\dfrac{m v}{k \sqrt{(M-m)}}\)
3 \(\dfrac{m v}{\sqrt{(M+m) k}}\)
4 \(\dfrac{m v}{k \sqrt{(M+m)}}\)
PHXI14:OSCILLATIONS

364389 The masses \(m_{1}\) and \(m_{2}\) are suspended together by a massless spring of constant \(k\). When the masses are in equilibrium, \(m_{1}\) is removed without disturbing the system; the amplitude of vibration is -

1 \(m_{2} g / k\)
2 \(m_{1} g / k\)
3 \(\dfrac{\left(m_{2}-m_{1}\right) g}{k}\)
4 \(\dfrac{\left(m_{1}+m_{2}\right) g}{k}\)