A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resulting amplitude is equal to the amplitude of individual motions, the phase difference between them will be:
1.
2.
3.
4.
Two simple pendulums have time periods T and . They start vibrating at the same instant from the mean position in the same phase. The phase difference between them when bigger pendulum completes one oscillation will be:
1.
2.
3.
4.
There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is T. If the resultant acceleration becomes g/4, then the new time period of the pendulum is
(1) 0.8 T
(2) 0.25 T
(3) 2 T
(4) 4 T
When two displacements represented by y1=asin(ωt) and y2=bcos(ωt) are superimposed,the motion is -
(1) not a simple harmonic
(2) simple harmonic with amplitude a/b
(3) simple harmonic with amplitude
(4) simple harmonic with amplitude (a+b)/2
An SHM has an amplitude \(a\) and a time period \(T.\) The maximum velocity will be:
1. \({4a \over T}\)
2. \({2a \over T}\)
3. \({2 \pi \over T}\)
4. \({2a \pi \over T}\)
The angular velocities of three bodies in simple harmonic motion are with their respective amplitudes as . If all the three bodies have same mass and maximum velocity, then
(a) (b)
(b) (d)
The amplitude of a particle executing SHM is 4 cm. At the mean position the speed of the particle is 16 cm/sec. The distance of the particle from the mean position at which the speed of the particle becomes will be
(1)
(2)
(3) 1 cm
(4) 2 cm
The maximum velocity of a simple harmonic motion represented by is given by
(1) 300
(2)
(3) 100
(4)
The displacement equation of a particle is The amplitude and maximum velocity will be respectively
(a) 5, 10
(b) 3, 2
(c) 4, 2
(d) 3, 4
The instantaneous displacement of a simple pendulum oscillator is given by . Its speed will be maximum at time
(1)
(2)
(3)
(4)
The displacement of a particle moving in S.H.M. at any instant is given by . The acceleration after time (where T is the time period) -
1.
2.
3.
4.
The amplitude of a particle executing S.H.M. with frequency of 60 Hz is 0.01 m. The maximum value of the acceleration of the particle is
(a) (b)
c) (d)
The displacement of an oscillating particle varies with time (in seconds) according to the equation .The maximum acceleration of the particle is approximately
(a) (b)
(c) (d)
A particle moving along the x-axis executes simple harmonic motion, then the force acting on it is given by
(1) – A Kx
(2) A cos (Kx)
(3) A exp (– Kx)
(4) A Kx
What is the maximum acceleration of the particle doing the SHM where 2 is in cm
(a) (b)
(c) (d)
A man measures the period of a simple pendulum inside a stationary lift and finds it to be T sec. If the lift accelerates upwards with an acceleration , then the period of the pendulum will be
(1) T
(2)
(3)
(4)
A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period is given by , where is equal to
(1) g
(2) g-a
(3) g+a
(4)
If the length of second's pendulum is decreased by 2%, how many seconds it will lose per day?
1. 3927 sec
2. 3727 sec
3. 3427 sec
4. 864 sec
In a simple pendulum, the period of oscillation T is related to length of the pendulum l as:
1. = constant
2. = constant
3. = constant
4. = constant
A pendulum has time period T. If it is taken on to another planet having acceleration due to gravity half and mass 9 times that of the earth, then its time period on the other planet will be:
1. | \(\sqrt{\mathrm{T}} \) | 2. | \(T \) |
3. | \(\mathrm{T}^{1 / 3} \) | 4. | \(\sqrt{2} \mathrm{~T}\) |
A particle in SHM is described by the displacement equation If the initial position of the particle is 1 cm and its initial velocity is cm/s, what is its amplitude? (The angular frequency of the particle is )
(1) 1 cm
(2) cm
(3) 2 cm
(4) 2.5 cm
A simple pendulum hanging from the ceiling of a stationary lift has a time period T1. When the lift moves downward with constant velocity, then the time period becomes T2. It can be concluded that:
1. | \(T_2 ~\text{is infinity} \) | 2. | \(\mathrm{T}_2>\mathrm{T}_1 \) |
3. | \(\mathrm{T}_2<\mathrm{T}_1 \) | 4. | \(T_2=T_1\) |
If the length of a pendulum is made 9 times and mass of the bob is made 4 times, then the value of time period will become:
1. 3T
2. 3/2T
3. 4T
4. 2T
The time period of a simple pendulum of length L as measured in an elevator descending with acceleration is
(1)
(2)
(3)
(4)
The displacement of a particle varies according to the relation x = 4(cospt + sinpt). The amplitude of the particle is
(1) 8
(2) -4
(3) 4
(4)
If the displacement equation of a particle be represented by , the particle executes
(1) A uniform circular motion
(2) A uniform elliptical motion
(3) A S.H.M.
(4) A rectilinear motion
The displacement of a particle varies according to the relation The amplitude of the particle is
(1) 8
(2) – 4
(3) 4
(4)
A S.H.M. is represented by The amplitude of the S.H.M. is
(1) 10 cm
(2) 20 cm
(3) cm
(4) 50 cm
The displacement of a particle varies with time as (in cm). If its motion is S.H.M., then its maximum acceleration is -
(a)
(b)
(c)
(d)
The period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination , is given by -
1.
2.
3.
4.
The displacement y of a particle executing periodic motion is given by This expression may be considered to be a result of the superposition of ........... independent harmonic motions
1. Two
2. Three
3. Four
4. Five
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10 s it will decrease to times its original magnitude, where equals
1. 0.7
2. 0.81
3. 0.729
4. 0.6
A particle performs SHM on x-axis with amplitude A and time period T. The time taken by the particle to travel a distance starting from rest is-
1.
2.
3.
4.
Two simple pendulums of length 5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed how many oscillations?
1. 5
2. 1
3. 2
4. 3
The figure shows the circular motion of a particle which is at the topmost point on the y-axis at t=0. The radius of the circle is B and the sense of revolution is clockwise. The time period is indicated in the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is:
(1) x(t) = Bsin
(2) x(t) = Bcos
(3) x(t) = Bsin
(4) x(t) = Bcos
The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and the ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3 , the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbon dioxide will be close to (ln 5 = 1.601, ln 2 = 0.693) :
(1) 231 s
(2) 208 s
(3) 161 s
(4) 142 s
A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x = cos, and y = traces a curve given by:
(1)
(2)
(3)
(4)
The angular frequency of the damped oscillator is given by, where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio is 8%, the change in the time period compared to the undamped oscillator is approximately as follows:
(1) increases by 1%
(2) increases by 8%
(3) decreases by 1%
(4) decreases by 8%
A pendulum with a time period of 1s is losing energy due to damping. At a certain time, its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant is:
(1)
(2)
(3) 2
(4)
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are the same and equal to A and T, respectively. At time t = 0 one particle has displacement A while the other one has displacement -A/2 and they are moving towards each other. If they cross each other at time t, then t is:
(1) T/6
(2) 5T/6
(3) T/3
(4) T/4
A block of mass 0.1 kg is connected to an elastic spring constant 640 and oscillates in a damping medium of damping constant . The system dissipates its energy gradually. The time taken for its mechanical energy of vibrations to drop to half of its initial value is closest to:
1. 2s
2. 3.5 s
3. 5 s
4. 7 s
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half of its value for every 10 oscillations. The time it will take to drop to of the original amplitude is close to:
1. 100 s
2. 20 s
3. 10 s
4. 50 s
A simple pendulum oscillating in air has time period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:
1,
2.
3.
4.
The displacement of a damped harmonic oscillator is given by
. Here t is in seconds. The time taken for its amplitude of vibrations to drop to half of its initial value is close to:
1. 13 s
2. 7 s
3. 27 s
4. 4 s
Which of the following option gives the correct categorization of hormones according to their chemical nature?
A Steroid |
B Amino-acid derivative |
C Iodothyromines |
|
1. |
Epinephrine, nor-epinephrine |
Estradiol, progesterone |
Thyroxine |
2. |
Estradiol, progesterone |
Epinephrine, nor-epinephrine |
Thyroxine |
3. |
Estradiol, epinephrine |
Nor-epinephrine progesterone |
Thyroxine |
4. |
Estradiaol, pogesterone |
Thyroxine |
Epinephrine, nor-epinephrine |