# SHM expression

## Trending Questions

**Q.**Out of the following functions representing motion of a particle which represent S.H.M?

I. y=sin ωt−cos ωt

II. y=sin3 ωt

III. y=5 cos (3π4−3ωt)

IV. y=1+ω2t2+ωt

- Only (IV) does not represent S.H.M.
- (I) and (III)
- (I) and (II)
- Only (I)

**Q.**The displacement y of a particle varies with time t according to the relation y=asinωt+bcosωt. Which of the following statement(s) is/are correct regarding the motion?

- The motion is SHM.
- The motion is SHM with amplitude a+b.
- The motion is SHM with amplitude a2+b2.
- The motion is SHM with amplitude √a2+b2.

**Q.**A block of mass 100 g attached to a spring of spring constant 100 N/m. The block is moved to compress the spring by 10 cm and then released on a frictionless floor as shown below. If the collisions with the wall in the front are elastic in nature, then the time period of the motion is

- 0.2 s
- 0.1 s
- 0.15 s
- 0.132 s

**Q.**Two pendulums of time periods 3 s and 7 s respectively start oscillating simultaneously from two opposite extreme positions. After how much time they will be in same phase?

- 218 s
- 214 s
- 212 s
- 2110 s

**Q.**A point moves along x-axis according to the equation x=Asin2(ωt−π4). Find the amplitude, period and velocity as a function of x.

- A2, πω, 2ω√(A−x)x
- 3A2, πω, ω√(A−x)x
- 3A2, πω, 3ω√(A−x)x
- A2, 2πω, 2ω√(A−x)x

**Q.**In order that the resultant path on superimposing two mutually perpendicular SHM be a circle, the conditions are that:

- the amplitudes on both SHM should be equal and they should have a phase difference of π2
- the amplitudes should be in the ratio 1:2 and the phase difference should be zero
- the amplitudes should be in the ratio 1:2 and the phase difference should be π2
- the amplitudes should be equal and the phase difference should be zero

**Q.**The displacement - time (x−t) graph of a particle executing simple harmonic motion is shown in figure. The correct variation of net force F acting on the particle as a function of time is

**Q.**A particle executing SHM has maximum acceleration of 2π m/s2 and maximum velocity of 6 m/s. Find its time period

- π22 s
- 2π23 s
- 6 s
- π3 s

**Q.**A particle performs SHM in a straight line. In the first second, starting from rest, it travels a distance a and in the next second, it travels a distance b on the same side of the mean position. The amplitude of the SHM is

- a−b
- 2a−b3
- 2a23a−b
- None of these

**Q.**Two particles are executing S.H.M of the same amplitude of 20 cm with the same period along the same line about the same equilibrium position. The maximum distance between the two is 20 cm. Their phase difference (in radians) is equal to

- π3
- π2
- 2π3
- 4π5

**Q.**If x, v and a denotes the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T. Then which of the following does not change with time?

- a2T2+4π2v2
- aT/x
- aT+2πv
- aT/v

**Q.**Two SHM’s are represented by the equations, y1=0.1sin(100πt+π3) and y2=0.1cos100πt. The phase difference between the speeds of the two particles is,

- π3
- π8
- π6
- π4

**Q.**Two particles are executing SHM, one with angular frequency ω and the other with ′2ω′. Which of the following acceleration (a) vs position (x) graphs correctly represent SHM's of two particles.

**Q.**

The co-ordinates of a moving particle are $\mathrm{x}={\mathrm{at}}^{2}$ and $\mathrm{y}={\mathrm{bt}}^{2}$, where $\mathrm{a}$ and $\mathrm{b}$ are constants. the velocity of a particle at any instant is

$2\mathrm{t}\sqrt{{\mathrm{a}}^{2}}++{\mathrm{b}}^{2}$

$2\mathrm{t}\left(\mathrm{a}+\mathrm{b}\right)$

$2\mathrm{t}\sqrt{{\mathrm{a}}^{2}+{\mathrm{b}}^{2}}$

$\sqrt{{\mathrm{a}}^{2}+{\mathrm{b}}^{2}}$

**Q.**

Which of the following equations can be that of an SHM? Here, x represents displacement from mean position.

t represents time

k is a positive constant

v represents velocity

md2xdt2−kx=0

md2xdt2+kx=0

mdvdt+kx=0

K∫t0vdt=−md2xdt2 .

**Q.**If x, v and a denotes the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T. Then which of the following does not change with time?

- a2T2+4π2v2
- aT/x
- aT+2πv
- aT/v

**Q.**A transverse sinusoidal wave moves along a string in the positive x−direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snapshot of the wave is shown in the figure. The velocity of a particle at P when its displacement is 5 cm along y−axis is

- √3π50^j m/s
- −√3π50^j m/s
- √3π50^i m/s
- −√3π50^i m/s

**Q.**In a horizontal spring mass system, mass m is released after being displaced towards right by some distance at t=0 on a frictionless surface. The phase angle of the motion in radian when it passes through the equilibrium position for the first time is

- π2
- π
- 3π2
- 0

**Q.**

A particle executing simple harmonic motion along y-axis has its motion described by the equation. y=Asin(ωt)+B. The amplitude of the simple harmonic motion is

A

B

A+B

√A+B

**Q.**Which of the following expressions represent simple harmonic motion?

- x=a sin (ωt+ϕ)
- x=a cos (ωt+δ)
- x=a sin ωt+b cos ωt
- x=a sin ωt cos ωt

**Q.**A particle executes linear SHM with a time period of 10 s. Find the time taken by the particle to go directly from its mean position (at t=0) to 12 of its amplitude.

- 56 s
- 5π6 s
- 1.2 s
- 53 s

**Q.**A particle ís executing simple harmonic motion with amplitude of 0.1 m. At a certain instant when its displacement is 0.02 m, its acceleration is 0.5 ms−2. The maximum velocity of the particle is (in ms−1)

- 0.01
- 0.05
- 0.5
- 0.25

**Q.**The displacement y of a particle varies with time t according to the relation y=asinωt+bcosωt. Which of the following statement(s) is/are correct regarding the motion?

- The motion is SHM.
- The motion is SHM with amplitude a+b.
- The motion is SHM with amplitude a2+b2.
- The motion is SHM with amplitude √a2+b2.

**Q.**A particle is placed at the lowest point of a smooth wire frame in the shape of a parabola, lying in the vertical xy− plane having equation x2=5y, where (x, y) are in metres. After slight displacement, the particle is set free to move. Find the angular frequency of oscillation in rad/s.

[Take g=10 m/s2)]

- 2 rad/s
- 4 rad/s
- 6 rad/s
- 8 rad/s

**Q.**

A test tube of cross-sectional area a has some lead shots in it. The total mass is m. It floats upright in a liquid of density d. When pushed down a little and released, it oscillates up and down with a period T. Choose the correct relationship from the following.

T=2π√magd

T=2π√mgad

T=2π√mdag

T=2π√magd

**Q.**Two blocks A(5 kg) and B(2 kg) attached to the ends of a spring of spring constant 1120 N/m are placed on a smooth horizontal plane with spring undeformed. Simultaneously velocities of 3 m/s and 10 m/s along the line of the spring in the same direction are imparted to A and B then

- the amplitude of oscillation of 5 kg block is 0.18 m
- the first maximum compression occurs after start at 3π56 s
- the maximum extension of the spring is 0.50 m
- time period of oscillation is π14 s

**Q.**If the period of S.H.M. is 12 seconds and amplitude 10 cm. What is the displacement 14 Seconds after passage of the particle through its extreme positive displacement?

- 5 cm
- 4 cm
- 2 cm
- 10 cm

**Q.**A large horizontal surface is in SHM with an amplitude of 1 cm. A mass of 10 kg is kept gently on it when it is at mean position. For the mass to always remain in contact with the surface, the maximum frequency of SHM will be

- 5 Hz
- 6 Hz
- 7 Hz
- 8 Hz

**Q.**Choose the correct statement (s) from the following in which k is a real, positive constant.

- Function f(t) = sin kt + coskt is simple harmonic having a period 2πk
- Function f(t) = sin πt+2 cos 2π+3 sin 3 πt is periodic but not simple harmonic having a period of 2s
- Function f(t) = cos kt+2 sin2kt is simple harmonic having a period 2πk.
- Function f(t) = e−kt is not periodic.

**Q.**A particle is executing SHM according to the equation, x=Acosωt. Average speed of the particle during the interval 0≤t≤π6ω is

- √3Aω2
- √3Aω4
- 3Aωπ
- 3Aωπ(2−√3)