-
question_answer1)
The phase of a particle executing simple harmonic motion is \[\frac{\pi }{2}\] when it has [MP PET 1985]
A)
Maximum velocity done
clear
B)
Maximum acceleration done
clear
C)
Maximum energy done
clear
D)
Maximum displacement done
clear
View Solution play_arrow
-
question_answer2)
A particle starts S.H.M. from the mean position. Its amplitude is A and time period is T. At the time when its speed is half of the maximum speed, its displacement y is [Haryana CEE 1996; CBSE PMT 1996; MH CET 2002]
A)
\[\frac{A}{2}\] done
clear
B)
\[\frac{A}{\sqrt{2}}\] done
clear
C)
\[\frac{A\sqrt{3}}{2}\] done
clear
D)
\[\frac{2A}{\sqrt{3}}\] done
clear
View Solution play_arrow
-
question_answer3)
The amplitude and the periodic time of a S.H.M. are 5cm and 6sec respectively. At a distance of 2.5cm away from the mean position, the phase will be
A)
\[5\pi /12\] done
clear
B)
\[\pi /4\] done
clear
C)
\[\pi /3\] done
clear
D)
\[\pi /6\] done
clear
View Solution play_arrow
-
question_answer4)
Two equations of two S.H.M. are \[y=a\sin \,(\omega \,t-\alpha )\] and\[y=b\cos (\omega \,t-\alpha )\]. The phase difference between the two is [MP PMT 1985]
A)
0° done
clear
B)
a° done
clear
C)
90° done
clear
D)
180° done
clear
View Solution play_arrow
-
question_answer5)
The amplitude and the time period in a S.H.M. is 0.5 cm and 0.4 sec respectively. If the initial phase is \[\pi /2\] radian, then the equation of S.H.M. will be
A)
\[y=0.5\sin 5\pi t\] done
clear
B)
\[y=0.5\sin 4\pi t\] done
clear
C)
\[y=0.5\sin 2.5\pi t\] done
clear
D)
\[y=0.5\cos 5\pi t\] done
clear
View Solution play_arrow
-
question_answer6)
The equation of S.H.M. is \[y=a\sin (2\pi nt+\alpha )\], then its phase at time t is [DPMT 2001]
A)
\[2\pi nt\] done
clear
B)
\[\alpha \] done
clear
C)
\[2\pi nt+\alpha \] done
clear
D)
\[2\pi t\] done
clear
View Solution play_arrow
-
question_answer7)
A particle is oscillating according to the equation\[X=7\cos 0.5\pi t\], where t is in second. The point moves from the position of equilibrium to maximum displacement in time [CPMT 1989]
A)
4.0 sec done
clear
B)
2.0 sec done
clear
C)
1.0 sec done
clear
D)
0.5 sec done
clear
View Solution play_arrow
-
question_answer8)
A simple harmonic oscillator has an amplitude a and time period T. The time required by it to travel from x = a to x = a / 2 is [CBSE PMT 1992; SCRA 1996; BHU 1997]
A)
T / 6 done
clear
B)
T / 4 done
clear
C)
T / 3 done
clear
D)
T / 2 done
clear
View Solution play_arrow
-
question_answer9)
Which of the following expressions represent simple harmonic motion [Roorkee 1999]
A)
\[x=A\sin (\omega \,t+\delta )\] done
clear
B)
\[x=B\cos (\omega \,t+\varphi )\] done
clear
C)
\[x=A\tan (\omega \,t+\varphi )\] done
clear
D)
\[x=A\sin \omega \,t\cos \omega \,t\] done
clear
View Solution play_arrow
-
question_answer10)
A \[1.00\times {{10}^{-20}}kg\] particle is vibrating with simple harmonic motion with a period of \[1.00\times {{10}^{-5}}sec\] and a maximum speed of \[1.00\times {{10}^{3}}m/s\]. The maximum displacement of the particle is [AMU (Med.) 1999]
A)
1.59 mm done
clear
B)
1.00 m done
clear
C)
10 m done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer11)
The phase (at a time t) of a particle in simple harmonic motion tells [AMU (Engg.) 1999]
A)
Only the position of the particle at time t done
clear
B)
Only the direction of motion of the particle at time t done
clear
C)
Both the position and direction of motion of the particle at time t done
clear
D)
Neither the position of the particle nor its direction of motion at time t done
clear
View Solution play_arrow
-
question_answer12)
A particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true [AMU (Engg.) 1999]
A)
The particle so moving executes S.H.M. done
clear
B)
The projection of the particle on any one of the diameters executes S.H.M. done
clear
C)
The projection of the particle on any of the diameters executes S.H.M. done
clear
D)
None of the above done
clear
View Solution play_arrow
-
question_answer13)
A particle is executing simple harmonic motion with a period of T seconds and amplitude a metre. The shortest time it takes to reach a point \[\frac{a}{\sqrt{2}}m\] from its mean position in seconds is [EAMCET (Med.) 2000]
A)
T done
clear
B)
T/4 done
clear
C)
T/8 done
clear
D)
T/16 done
clear
View Solution play_arrow
-
question_answer14)
A simple harmonic motion is represented by \[F(t)=10\sin \,(20\,t+0.5)\]. The amplitude of the S.H.M. is [DPMT 1998; CBSE PMT 2000; MH CET 2001]
A)
a = 30 done
clear
B)
a = 20 done
clear
C)
a = 10 done
clear
D)
a = 5 done
clear
View Solution play_arrow
-
question_answer15)
Which of the following equation does not represent a simple harmonic motion [Kerala (Med.) 2002]
A)
\[y=a\sin \omega \,t\] done
clear
B)
\[y=a\cos \omega \,t\] done
clear
C)
\[y=a\sin \omega \,t+b\cos \omega \,t\] done
clear
D)
\[y=a\tan \omega \,t\] done
clear
View Solution play_arrow
-
question_answer16)
A particle in S.H.M. is described by the displacement function \[x(t)=a\cos (\omega t+\theta )\]. If the initial \[(t=0)\] position of the particle is 1 cm and its initial velocity is \[\pi \,cm/s\]. The angular frequency of the particle is \[\pi \,rad/s\], then it?s amplitude is [AMU (Med.) 2002]
A)
1 cm done
clear
B)
\[\sqrt{2}\,cm\] done
clear
C)
2 cm done
clear
D)
2.5 cm done
clear
View Solution play_arrow
-
question_answer17)
A particle executes a simple harmonic motion of time period T. Find the time taken by the particle to go directly from its mean position to half the amplitude [UPSEAT 2002]
A)
T / 2 done
clear
B)
T / 4 done
clear
C)
T / 8 done
clear
D)
T / 12 done
clear
View Solution play_arrow
-
question_answer18)
A particle executing simple harmonic motion along y-axis has its motion described by the equation \[y=A\sin (\omega \,t)+B\]. The amplitude of the simple harmonic motion is [Orissa JEE 2003]
A)
A done
clear
B)
B done
clear
C)
A + B done
clear
D)
\[\sqrt{A+B}\] done
clear
View Solution play_arrow
-
question_answer19)
A particle executing S.H.M. of amplitude 4 cm and T = 4 sec. The time taken by it to move from positive extreme position to half the amplitude is [BHU 1995]
A)
1 sec done
clear
B)
1/3 sec done
clear
C)
2/3 sec done
clear
D)
\[\sqrt{3/2}\]sec done
clear
View Solution play_arrow
-
question_answer20)
Which one of the following is a simple harmonic motion [CBSE PMT 1994]
A)
Wave moving through a string fixed at both ends done
clear
B)
Earth spinning about its own axis done
clear
C)
Ball bouncing between two rigid vertical walls done
clear
D)
Particle moving in a circle with uniform speed done
clear
View Solution play_arrow
-
question_answer21)
A particle is moving in a circle with uniform speed. Its motion is [CPMT 1978; CBSE PMT 2005]
A)
Periodic and simple harmonic done
clear
B)
Periodic but not simple harmonic done
clear
C)
A periodic done
clear
D)
None of the above done
clear
View Solution play_arrow
-
question_answer22)
Two simple harmonic motions are represented by the equations \[{{y}_{1}}=0.1\sin \left( 100\pi t+\frac{\pi }{3} \right)\]and \[{{y}_{2}}=0.1\cos \pi t.\] The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is [AIEEE 2005]
A)
\[\frac{-\pi }{3}\] done
clear
B)
\[\frac{\pi }{6}\] done
clear
C)
\[\frac{-\pi }{6}\] done
clear
D)
\[\frac{\pi }{3}\] done
clear
View Solution play_arrow
-
question_answer23)
Two particles are executing S.H.M. The equation of their motion are \[{{y}_{1}}=10\sin \left( \omega \,t+\frac{\pi T}{4} \right),\]\[{{y}_{2}}=25\sin \,\left( \omega \,t+\frac{\sqrt{3}\pi T}{4} \right)\]. What is the ratio of their amplitude [DCE 1996]
A)
1 : 1 done
clear
B)
2 : 5 done
clear
C)
1 : 2 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer24)
The periodic time of a body executing simple harmonic motion is 3 sec. After how much interval from time t = 0, its displacement will be half of its amplitude [BHU 1998]
A)
\[\frac{1}{8}\]sec done
clear
B)
\[\frac{1}{6}\]sec done
clear
C)
\[\frac{1}{4}\]sec done
clear
D)
\[\frac{1}{3}\]sec done
clear
View Solution play_arrow
-
question_answer25)
A system exhibiting S.H.M. must possess [KCET 1994]
A)
Inertia only done
clear
B)
Elasticity as well as inertia done
clear
C)
Elasticity, inertia and an external force done
clear
D)
Elasticity only done
clear
View Solution play_arrow
-
question_answer26)
If \[x=a\sin \left( \omega t+\frac{\pi }{6} \right)\] and \[{x}'=a\cos \omega t\], then what is the phase difference between the two waves [RPET 1996]
A)
p / 3 done
clear
B)
p / 6 done
clear
C)
p / 2 done
clear
D)
p done
clear
View Solution play_arrow