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Oscillations Test - 46

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Oscillations Test - 46
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  • Question 1
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    Three simple harmonic motions in the same direction having the same amplitude a and same period are superposed. If each differs in phase from the next by 45°, then
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  • Question 2
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    A linear harmonic oscillator of force constant 2 × 106 N/m times and amplitude 0.01 m has a total mechanical energy of 160 joules. Its
    Solution

  • Question 3
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    A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits –ɸ and + ɸ. For an angular displacement θ ( |θ| < ɸ ), the tension in the string and the velocity of the bob are T and v respectively. The following relations hold good under the above conditions
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  • Question 4
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    Which of the following expressions represent simple harmonic motion
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  • Question 5
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    A metal rod of length L and mass ‘M’ is pivoted at one end. A thin disk of mass ‘M\' and radius \'R’ (< L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached (case A). The disc is not free to rotate about its centre and (case B) the disc is free to rotate about its centre. The rod-disc system performs S.H.M. in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true

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  • Question 6
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    If two springs S1 and S2 of force constants k1 and k2, respectively, are stretched by the same force, it is found that more work is done on spring S1 than on spring S2.
    Statement 1 If stretched by the same amount, work done on S1, will be more than that on S2
    Statement 2 : k1 < k2
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  • Question 9
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  • Question 10
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    Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is x(t) vs. p(t) curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative.
    The phase space diagram for a ball thrown vertically up from ground is

    Solution

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