Relating Circular Motion to SHM

Q.

A simple harmonic oscillator has an amplitude a and time period T. The time required by it to travel from x = a to x = $\frac{a}{2}$ is

[CBSE PMT 1992; SCRA 1996; BHU 1997]

1. T/6

2. T/4

3. T/3

4. T/2

Q.

The maximum velocity and the maximum acceleration of a body moving in a

simple harmonic oscillator are 2 m/s and 4 m/$s^2$. Then angular velocity will be

[Pb. PMT 1998; MH CET 1999, 2003]

1. 0.5 rad/sec

2. 1 rad/sec

3. 2 rad/sec

4. 3 rad/sec

Q. the velocity of a particle is given by v=at^2+bt+c, where v is in m/s, time t is in second abd a b, c are the cons†an ts. the unit of the quantity abc is

Q.

Which of the following equation does not represent a simple harmonic motion

1. 

2. 

3. 

4. 

Q. 9.The angular amplitude of a simple pendulum is a .what is the maximum tension in the string ?

Q. The position of a particle expressed as r=(2t3i^+tj^) m, where t is in second The average velocity during first 2 second starting from t=0 and origin is given by

Q. The velocity of a particle is given by v vector equals to 3 i cap plus 6 t j cap metre per second , where t is in seconds the equation of trajectory of particle is

Q.

A particle is vibrating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is its energy half potential and half kinetic

[NCERT 1984; MNR 1995;

RPMT 1995; DCE 2000; UPSEAT 2000]

1. 1 cm

2. 

3. 3 cm

4. 

Q. Two identical pendulums oscillate with a constant phase difference pi/4 and same amplitude if the maximum velocity of one is v the maximum velocity of the other will be

Q. A pendulum oscillates simple harmonically if and only if (I) the size of the bob of pendulum is negligible in comparison with the length of the pendulum (II) the angular amplitude is less than 10° (A) Both (I) and (II) are correct (B) Both (I) and (II) are incorrect (C) Only (I) is correct (D) Only (II) is correct

Q. To determine acceleration due to gravity, the time of 20 oscillations of a simple pendulum of length100 cm was observed to be 40 s. Calculate the value ofg and maximum percentage error in themeasured value of g.

Q. Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial (t =0) position of the particle, the radius of the circle, OSCILLATIONS 365 and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: (x is in cm and t is in s). (a) x = –2 sin (3t + π /3) (b) x = cos (π /6 – t) (c) x = 3 sin (2π t + π /4) (d) x = 2 cos π t

Q. the position of a body moving in straight line is x=[2traised2 +2t +9] where x is in meter and t is in second the velocity v n[v=dx/dt] of the body at t=1s is

Q. out of two cars A and B car A is moving towards east with velocity of 10m/s whereas B is moving towards north with a velocity of 20m/s then velocity of A w.r.t B

Q. At t=0, a particle at the origin has a velocity of 15m/s at 37^° above the horizontal x axis. at t=5s, it is at x=20m and y=35m and its velocity is 30m/s at 53^° above the horizontal .find a) its average velocity b) its average acceleration

Q. A simple pendulum is oscillating with an angular amplitude 60^°. If mass of bob is 50 gram then the tension in the string at mean position is (g =10 m/s^2

Q. Particle A is moving with velocity 6i+ 10j and particle B is moving with velocity 3i +6j magnitude of velocity of A wet B is

Q. Figures 14.25 correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure. Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.

Q.

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

[DPMT 1998; CBSE PMT 1999; AFMC 2001;

Pb. PMT 2001; Pb. PET 2001, 02; CPMT 1993, 95, 04;

RPMT 2005; MP PMT 2005]

1. 

2. 

3. 

4. 

Q. a body is moving towards north with initial velocity of 13m/sec .It is subjected to a retardation of 2m/sec^2 towards south .the dis†an ce travelled by it in 7th second is 1)zero 2)0.75m 3)0.5m 4)0.25

Q. 69.For a body moving with uniform acceleration- a. Initial and final velocities in a time interval - t are u and v respectively. Then its average velocity in the time interval t is?

Q. 65. When the maximum KE of a simple pendulum is K, then what is the displacement (in terms if amplitude) when its KE is K/2 1) a/(root)2 2) a/2 3) a/(root)3 4) a/3

Q. A particle moves along a horizontal line with acceleration proportional to cos t, where t is time. When t = 0, velocity is u, and position is x=0. When t = π/2, v = 2u. Find the total distance particle has travelled when t = 2π.

Q. A particle moves in a circular path with a uniform speed. Its motion is

1. periodic
2. oscillatory
3. simple harmonic
4. angular simple harmonic

Q. The velocity of a body varies with time as V=(4t^3+2/t^2+1) m/s, the displacement of particle from t = 1 to t = 2 s is??

Q. 132.The relation between time t and distance x is given as t= ax+bx where a and b are constants if the velocity of particle is v at a distance x then find retardation of the particle

Q. The position of a particle is given by r =3t i +2t²J +5k , where t is in second and the coefficients have the proper units for r to be in metre. Find the magnitude and direction of the velocity of the particle at t=3s.

Q. 75. A particle moving with a uniform acceleration travels 24 metre and 64 metre in first two successive intervalsof 4 second each. Its initial velocity is(1) 1 m/s(3) 5 m/s(2) 2 m/s(4) 10 m/s

Q. A particle moves in a circular path with a continuously increasing speed. Its motion is
(a) periodic
(b) oscillatory
(c) simple harmonic
(d) none of them

Q. 19. Velocity and acceleration of a particle at some instant of time are v=(3i+4j) m/s and a=-(6i+8j) m/s square respectively. At same instant particle is at origin.Maximum x-coordinate of particle will be: (A) 1.5metre (B) 0.75 metre (C) 2.25 metre (D) 4.0 metre