Problems on SHM
Q: A loudspeaker produces a musical sound by means of the oscillation of a diaphragm whose amplitude is limited to 1.00 μm. (a) At what frequency is the magnitude a of the diaphragm’s acceleration equal to g? (b) For greater frequencies, is ‘a’ greater than or less than g? Take g = 10 ms-2.
Q: What is the phase constant for the harmonic oscillator with the velocity function v(t) given in figure if the position function x(t) has the form x = Acos(ωt +ф)? The vertical axis scale is set by vs = 4 cm/s.
Q: The equation of motion of a particle started at t=0 is given by x = 10sin(10t + п/3), where x is in centimeter and t in second. When does the particle (a) first come to rest (b) first have zero acceleration (c) first have maximum speed?
Q: Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude (b) velocity to change value from half its maximum to maximum.
Q: A body of mass 2 kg suspended through a vertical spring executes simple harmonic motion of period 6 s. If the oscillations are stopped and the body hangs in equilibrium, find the potential energy stored in the spring. Use g = 10 ms-2.
Q: A particle is subjected to two simple harmonic motions, one along the x-axis and the other on a line making an angle of 45o with the x-axis. The two motions are given by
x= x0sinωt and s = s0sinωt
Find the amplitude of the resultant motion.
Q: In a damped oscillator with m = 500 g, k = 100 N/m, and b = 75 g/s, what is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles?
Q: A block of mass ‘m’ is suspended from the ceiling of a stationary standing elevator through a spring of spring constant ‘k’. Suddenly the cable breaks and the elevator starts falling freely. Show that the block now executes a simple harmonic motion in the elevator. Find the amplitude.
Q: A uniform rod of mass ‘m’ and length ‘l’ is suspended through a light wire of length ‘l’ and torsional constant ‘k’ as shown in figure. Find the time period if the system makes (a)small oscillations in the vertical plane about the suspension point and (b) angular oscillations in the horizontal plane about the center of the rod.
Q: A simple pendulum is suspended from the ceiling of a car accelerating uniformly on a horizontal road. If the acceleration is ‘a0’ and the length of the pendulum is ‘l ’, find the time period of small oscillations about the mean position.
Q: A damped harmonic oscillator consists of a block (m = 2 kg), a spring (k = 30 N/m), and a damping force (F = -bv). Initially, it oscillates with an amplitude of 25 cm; because of the
damping, the amplitude falls to three-fourths of this initial value at the completion of four oscillations. (a) What is the value of b? (b) How much energy has been “lost” during these four oscillations
Comments
Post a Comment