The displacement of a particle executing simple harmonic motion is given by
Then the amplitude of its oscillation is given by :
A+ B
Avearge velocity of a particle exceuting SHM in one complete vibration is :
zero
A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it travels 2a in same direction then:-
Screenshot_20190304-192117.png A train of sound waves is propagated along a wide pipe and it is reflected from an open end. If the amplitude of the waves is 0.002 cm, the frequency is 1000 Hz and the wavelength is 40 cm, the amplitude of vibration at a point 10 cm from open end inside the pipe will be
A pendulum clock (fitted with a small heavy bob
that is connected with a metal rod) is 5 seconds
fast each day at a temperature of 15^{0}C and
10 seconds slow at a temperature of 30^{0 }C. The
temperature at which it is designed to give correct
time is
@Ravindra
A particle is performing simple harmonic motion along x-axis with amplitude 4 cm and time period 1.2 sec. The minimum time taken by the particle to move from x =2 cm to x = + 4 cm and back again is given by
A) 0.6 sec
B) 0.4 sec
C) 0.3 sec
D) 0.2 sec
Answer: B
Solution :
Time taken by particle to move from x=0 (mean position) to x = 4 (extreme position)
Let t be the time taken by the particle to move from x=0 to x=2 cm
Hence time to move from x = 2 to x = 4 will be equal to 0.3 ?
0.1 = 0.2 s
Hence total time to move from x = 2 to x = 4 and back again
A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s^{2 }at a distance of 5 m from the mean position. The time period of oscillation is
2 s
s
2 s
1 s
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
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
Two waves are represented by the equations y_{1} = a sin (t + kx + 0.57) m and y_{2} = a cos (t + kx) m, where x is in meter and t in sec. The phase diference between them is
1.0 radian
1.25 radian
1.57 radian
0.57 radian
Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is
0
1
/6
Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to the occurrence of 6 beats/s when both the wires oscillate together would be
0.02
0.03
0.04
0.01
The oscillation of a body on a smooth horizontal surface is represented by the equation,
X = A cos ( t)
where, X = displacement at time t
= frequency of oscillation
Which one of the following graphs shows correctly the variation of 'a' with 't'?
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
The displacement of a particle along the x-axis is given by x = a sin^{2}t. The motion of the particle corresponds to:
simple harmonic motion of frequency /
simple harmonic motion of frequency 3/2
non simple harmonic motion
simple harmonic motion of frequency /2
Sound waves travel at 350 m/s through a warm air and at 3500 m/s through a warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air
decreases by a factor 10
increases by a factor 20
increases by a factor 10
decreases by a factor 20
A particle of mass m is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time