Physics-
General
Easy
Question
The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is
![](data:image/png;base64,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)
The correct answer is: ![fraction numerator k subscript 2 end subscript A over denominator k subscript 1 end subscript plus k subscript 2 end subscript end fraction](data:image/png;base64,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)
![x subscript 1 end subscript plus x subscript 2 end subscript equals A a n d k subscript 1 end subscript x subscript 1 end subscript equals k subscript 2 end subscript x subscript 2 end subscript o r fraction numerator x subscript 1 end subscript over denominator x subscript 2 end subscript end fraction equals fraction numerator k subscript 2 end subscript over denominator k subscript 1 end subscript end fraction](data:image/png;base64,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)
Solving these equations, we get
![x subscript 1 end subscript equals open parentheses fraction numerator k subscript 2 end subscript over denominator k subscript 1 end subscript plus k subscript 2 end subscript end fraction close parentheses A](data:image/png;base64,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)
Related Questions to study
Physics-
The displacement of a particle performing simple harmonic motion is given by,
where distance is in cm and time is in second. The amplitude of motion is
The displacement of a particle performing simple harmonic motion is given by,
where distance is in cm and time is in second. The amplitude of motion is
Physics-General
Physics-
Two simple harmonic motions are represented by
The ratio of their amplitudes is
Two simple harmonic motions are represented by
The ratio of their amplitudes is
Physics-General
Physics-
A 1000 Hz sound wave in air strikes the surface of a lake and penetrates into water. If speed of sound in water is
,the frequency and wavelength of waves in water are
A 1000 Hz sound wave in air strikes the surface of a lake and penetrates into water. If speed of sound in water is
,the frequency and wavelength of waves in water are
Physics-General
Physics-
Which of the following functions represent a wave?
Which of the following functions represent a wave?
Physics-General
Physics-
The Speed of sound in a mixture of 1 mole of helium and 2 moles of oxygen at
is
The Speed of sound in a mixture of 1 mole of helium and 2 moles of oxygen at
is
Physics-General
Physics-
A sound absorber the sound level by 20 dB. The intensity decreases by a factor of
A sound absorber the sound level by 20 dB. The intensity decreases by a factor of
Physics-General
Physics-
An object producing a pitch of 400 Hz flies past a stationary person. The object was moving in a straight line with a velocity
. What is the change in frequency noted by the person as the person as the object files past him?
An object producing a pitch of 400 Hz flies past a stationary person. The object was moving in a straight line with a velocity
. What is the change in frequency noted by the person as the person as the object files past him?
Physics-General
Physics-
A police car moving at
, changes a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.
![](data:image/png;base64,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)
A police car moving at
, changes a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.
![](data:image/png;base64,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)
Physics-General
Physics-
A motor cycle starts from rest and accelerates along a straight path at
. At the starting point of the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was rest? (Speed =330
)
A motor cycle starts from rest and accelerates along a straight path at
. At the starting point of the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was rest? (Speed =330
)
Physics-General
Physics-
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is
![](data:image/png;base64,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)
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAW0AAACYCAYAAAAvKbg8AAAJ40lEQVR4nO3dP1CbdRzH8U84vYQ7/6SLPNx5EroQO0UdpCwgg6Yu5lgEBwsOGhgUGHp1g6WlDlAdBB1oWSgsXKaQLm3qedecQ5tzsGGp6UR659noYJ8sjUMLJ/1DUyT88m3er7sed+V5ki/Lmx+/50kSqFarVQEATGhxPQAAoHZEGwAMIdoAYEigq6ururGx4XoOAA3A8zyl02m99dZbrkfBE7ywsbGhcDisWCzmehYcAN/39ccff+j111+v+ZxSqaRCoaBoNCrP8+o4HRpBa2ur6xGwi4Ckal9fny5fvux6FhyA0dFRLSwsaHNzs+YAnz9/XiMjIzp37pyGh4frPCGA3bCn3WR839/xFYAtRBsADCHaAGAI0QYAQ4g2ABhCtAHAEKINAIYQbQAwhGgDgCFEGwAMIdoAYAjRBgBDiDYAGEK0AcAQog0AhhBtADCEaAOAIUQbAAwh2gBgCNEGAEOINgAYQrQBwBCiDQCGEG0AMIRoA3BmZWVFMzMzrscwhWgDcObHH3/U9PS0qtWq61HMINoAnPE8T77vux7DuVKppHK5XNOxRBuAM6FQSJJULBYdT+LWwMCAhoaGavqLg2gDcOaNN95wPYJzvu8rl8tt/wJ7GqINwLlmXmkXCgVJUkdHR03HE20AzkQiEQUCgabe1976hdXV1VXT8UQbgHPNvNLe2NiQJEWjUQUCgaceT7QBOBOLxSRJv/zyS9Pe9nfr1i1J96NdC6INwJlYLKZwOKxsNut6FGfy+byCwaA8z6vpeKINwKl4PK5isdiUWyTlcln5fF59fX01n0O0ATj1/vvvKxAIKJVKuR7lwK2ursr3fX366ac1n0O0ATi1tcr86aefmm5fe2lpScFgUIlEoqaLkBLRBuBYJBJRNBpVNpttqlv/isWicrmcPv7445pfWCMRbQANIJFIqFwua2FhwfUoB2ZpaUmSdPz48ZpX2RLRBtAAvvzyS7W2tuqbb77R3bt3XY9Td77v64cfflBbW9szXYSUiDaABuB5npLJpEqlUlOsts+cOaNSqaTPP//8mc8l2gAawokTJ5pitV0sFnXmzBl1dHTo5MmTz7Q1IhFtAA2iWVbbY2Njunv3rmZnZ9Xa2vrM5xNtAA1ja7X93XffPZer7VQqpUwmo0QioUQisafHINoAGobneTpx4oSKxaLGxsaeq/u2fd/X2NiYgsGgvv/++2feFtlCtAE0lKmpKR07dkznz59/brZJfN/XwMCANjc3derUqZrfZ+RxiDaAhrO8vKzOzk5NTk7q6tWrrsf53z777DOtr68rHo8rmUzueZUtEW0ADSgcDmt5eVmBQECffPKJ7ty543qkPZucnNTKyoq6u7u1tra2p4uP/0W0ATSk7u5unTp1Srdu3dKHH35oMtzT09M6e/asurq6lE6n/3ewJaINoIGNj49reHhYuVxOPT09+v33312PVLOlpSVNT0+ro6ND6XRahw4d2pfHJdoAGtri4qImJiZUKBTU09Oj69evux5pV77va3JyUiMjI2pra1M6nVZnZ+e+PT7RBtDwZmdnNTc3p9u3b6u/v1/r6+uuR3qsUqmk/v5+zc3N6d1339W1a9f05ptv7utzEG0AJoyPj2txcVGVSkUDAwOan593PdIO2WxWb7/9tq5evaqvvvpKly5dUnt7+74/D9EGYMbw8LDW1tZ06NAhjY2N6ejRo85vCSyXy5qenlZ/f7/u3Lmj5eVlnT17dl8uOj4O0QZgSjwe182bN3Xy5Enl83n19PRoaGhIm5ubBzrHVqwPHz6sqakpdXV16dq1axoaGqrr8xJtAOaEQiGdPn1aN27c0LFjx7SysqIjR47o66+/rvsHBPu+r2+//XY71sFgUIuLi/rtt9/2ff/6cYg2ALMikYjS6bTW19fV3t6umZkZdXZ26ujRo1pYWFCpVNq358pkMpqYmFBnZ6fGx8cVDAY1OzurmzdvamRk5H+9yvFZvHAgzwIAdRSPxxWPx5XJZLS6uqpUKqXR0VGNjo4qkUiot7dXsVhMnucpGo3W9JjFYlGZTEYXL15UJpPZ/vxKz/M0OzurZDJZt33r3RBtAM+NrXjPz88rlUptBzyVSu04LhKJbH+gsCQVCoXt7xUKhUdW6N3d3froo48Uj8cVi8Xq/4PsgmgDeO6EQiENDg5qcHBQ5XJZ+Xxe2WxWlUpFuVxO5XJZ2WxW2Wx2x3nt7e2KRqPb/3p7exWPxxUOhx39JI8i2gCea+FwWH19fbt+gG6xWNThw4f1wQcfaHFx8cD2p/eCC5EAYAjRrlE2m93XK9EAsBdsjzxBoVBQNpvVxYsXtb6+rkqlonfeeUc///yzQqGQ6/EANCmi/cBWpK9cuaLLly/r9u3bjxzz8ssvE2wATjVttMvlsjKZjK5cuaJMJrPrq6haWlr04osv6ty5cwc4IQA8qqmi/d9I5/P57f9/2pXie/fuaXR0VJFIpN4jAsCumiLaExMTmp+fV6VSeez3q9XqUx/jwoULj9yg36impqZ0/Phx12MAqIOmuHtk66b6LXu5B7OR79t82EsvveR6BAB10hQr7evXr++40Pjw7XuBQOCpq+0vvvhCU1NT9R4VAHbVFCttSYpGo0omk7pw4YI2Nzd148YNzc/Pa3BwUG1tbTuOfXhV3dLSopmZmbq/5SMAPE3TRPthT4p4IpHQq6++uuPYe/fuqVKpaGRkxNG0AHBfU2yP1GLrDWKSyaQkbb/BzNZ923/99Zf++ecf+b7PvdoAnCHaTxCLxRSLxTQ+Pi7pfsQ9zyPYAJwi2jVy/R66ACA18Z42AFhEtAHAEKINAIYQbQAwhGgDgCFEGwAMIdoAYAjRBgBDiDYAGEK0AcAQog0AhhBtADCEaAOAIUQbAAwh2gBgCNEGAEOINgAYQrQBwBCiDQCGEG0AMIRoA4AhRBsADCHaAGAI0QYAQ4g2ABhCtAHAEKINAIYQbQAwhGgDgCFEGwAMIdoAYAjRBgBDiDYAGEK0AcAQog0AhhBtADCEaAOAIUQbAAwh2gCaXiQSUSKRUG9vrwKBgOtxdvWC6wEAoBGsra25HqEmrLQBwBCiDQCGEG0AMIRoA4AhRBsADCHaAGAI0QYAQ4g2ABhCtAHAEKINAIYQbQAwhGgDgCFEGwAMIdoAYAjRBgBDiDYAGEK0AcAQog0AhhBtADCEaAOAIUQbAAwJSKqGw2HFYjHXs+AAFAoFlUoldXd3KxQK1XTOn3/+qV9//VVHjhzRa6+9VucJ0UgikYhOnz4tz/Ncj4IHAq+88kr177//dj0HgAZ16dIlvffee67HwAOBarVadT0EDk4ul9Pq6qrm5uZcjwJgD4g2ABjChUgAMIRoA4AhRBsADCHaAGAI0QYAQ/4FAivcK1ijLg0AAAAASUVORK5CYII=)
Physics-General
Physics-
An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is
An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is
Physics-General
Physics-
In an experiment with sonameter a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. tension of the string remaining constant the frequency of the second tuning fork is
In an experiment with sonameter a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. tension of the string remaining constant the frequency of the second tuning fork is
Physics-General
Physics-
A uniform wire of length L, diameter D and density S is stretched under a tension T. the correct relation between its fundamental frequency f, the length L and the diameter D is
A uniform wire of length L, diameter D and density S is stretched under a tension T. the correct relation between its fundamental frequency f, the length L and the diameter D is
Physics-General
Physics-
If you set up the seven overtone on a string fixed at both ends, how many nodes and antinodes are set up in it?
If you set up the seven overtone on a string fixed at both ends, how many nodes and antinodes are set up in it?
Physics-General
Physics-
If in a resonance tube a oil of density higher than that water is used then at the resonance frequency would
If in a resonance tube a oil of density higher than that water is used then at the resonance frequency would
Physics-General