Damped & Forced Oscillations Resonance — Practice Questions
Free NEET Physics multiple-choice questions on Damped & Forced Oscillations Resonance. Attempt each question and reveal the answer with a full explanation.
In the case of forced oscillations, which of the following is true at resonance? The amplitude of oscillation is maximum. The phase difference between force and displacement is zero. The frequency of driving force is half the natural frequency. The energy of the system is minimum. The Quality factor Q of a damped oscillator is defined as the ratio of 2 times the energy stored to the energy lost per cycle. It is also equal to: Resonant frequency / Bandwidth Bandwidth / Resonant frequency Amplitude / Damping constant Damping constant / Mass The logarithmic decrement of a damped oscillator is the natural logarithm of the ratio of two successive amplitudes A n and A n+1 . If A = A 0 e -bt/2m , then is equal to (where T is the period): bT/2m b/2mT 2m/bT e -bT/2m In forced oscillations, at very high frequencies (much higher than the natural frequency), the phase difference between the driving force and the displacement is approximately: radians 0 radians /2 radians /4 radians In a damped harmonic oscillator, the total mechanical energy E decreases with time t as: E = E 0 e -bt/m E = E 0 e -bt/2m E = E 0 e -2bt/m E = E 0 e -b 2t/m Each of the two strings of length 51.6 cm and 49.1 cm are tensioned separately by 20 N force. Mass per unit length of both the strings is same and equal to 1 g/m. When both the strings vibrate simultaneously the number of beats is : 3 5 7 8 A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is 254 Hz 246 Hz 240 Hz 260 Hz If n 1 , n 2 and n 3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by :- 1 n = 1 n 1 + 1 n 2 + 1 n 3 1 n = 1 n 1 + 1 n 2 + 1 n 3 n = n 1 + n 2 + n 3 n=n 1+n 2+n 3 The number of possible natural oscillation of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are : (velocity of sound = 340 ms -1 ) 4 5 7 6 Two open organ pipes of fundamental frequencies n 1 and n 2 are joined in series. The fundamental frequency of the new pipe so obtained will be : (n 1+n 2) n 1+n 2 2 n 1 2+n 2 2 n 1n 2 n 1+n 2 The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is 12.5 cm 8 cm 13.2 cm 16 cm At resonance, the amplitude of a forced oscillator is: Maximum Minimum Zero Independent of frequency A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is 350 m/s 339 m/s 330 m/s 300 m/s In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz . When tension in B is slightly decreased, the beat frequency increases to 7 Hz . If the frequency of A is 530 Hz , the original frequency of B will be: 524 Hz 536 Hz 537 Hz 523 Hz In a damped oscillation, the amplitude of oscillation at any time t is given by A = A 0 e -bt/2m . The time in which the amplitude reduces to half its initial value is: 2m 2 b m 2 b b 2 2m 2m b 2 The Quality factor ( Q ) of a damped oscillator is related to the damping constant b and mass m as: Q = m 0 b Q = b m 0 Q = 2m b Q = m b 0 For a driven (forced) harmonic oscillator, the phase difference between the driving force and the displacement at resonance is: /2 0 /4 In a damped harmonic oscillator, the amplitude after 50 oscillations is 0.8A 0 . The amplitude after 100 oscillations will be: 0.64A 0 0.60A 0 0.40A 0 0.72A 0 In a forced oscillation, if the frequency of the driving force is much greater than the natural frequency of the system, the phase difference between the displacement and the force is approximately: 0 /2 /4 In a damped harmonic oscillator, the mechanical energy E decreases exponentially with time. If the time constant for amplitude is , the time after which the energy becomes 1/e 2 of its initial value is: 2 /2 4 For a forced oscillator, the amplitude of vibration is maximum when: The external frequency is equal to the natural frequency. The damping constant is very high. The external frequency is much greater than the natural frequency. The external force is zero. Two vibrating tuning forks produce progressive waves given by Y 1=4 500 t and Y 2=2 506 t Number of beats produced per minute is 3 360 180 60 If we study the vibration of a pipe open at both ends, then the following statement is not true Open end will be anti-node Odd harmonics of the fundamental frequency will be generated All harmonics of the fundamental frequency will be generated Pressure change will be maximum at both ends An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is : 66.7 cm 100 cm 150 cm 200 cm A metal rod of 1m length, is dropped exact vertically on to a hard metal floor. With an oscilloscope, it is determined that the impact produces a longitudinal wave of 1.2k Hz frequency. The speed of sound in the metal rod is : 600 m/s 2400 m/s 1800 m/s 1200 m/s The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is 1 : 2 2 : 1 1 : 3 3 : 1 The amplitude of a damped oscillator becomes half of its initial value A 0 after 2 seconds. After 6 seconds, its amplitude will be: A 0/8 A 0/4 A 0/6 A 0/12