List of top Physics Questions on simple harmonic motion asked in CBSE Class XI

A Cylindrical piece of cork of density of base area A and height h floats in a liquid of density \(\rho_l\) .The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period
\(T\) = \(2π\sqrt{\frac{h\rho}{\rho_lg}}\)
Where \(\rho\) is the density of cork. (Ignore damping due to viscosity of the liquid).

One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic motion.

The motion of a particle executing simple harmonic motion is described by the displacement function, 
x(t) = A cos (ωt + φ ). 
If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, what are its amplitude and initial phase angle ? The angular frequency of the particle is π s–1. If instead of the cosine function, we choose the sine function to describe the SHM : x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial conditions.

Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion? 

(a) a=0.7x 

(b) a= –200x 2 

(c) a=–10x 

(d) a=100x 3

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is 

(a) at the end A, 

(b) at the end B, 

(c) at the mid-point of AB going towards A, 

(d) at 2 cm away from B going towards A, 

(e) at 3 cm away from A going towards B, and 

(f) at 4 cm away from B going towards A

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (ω is any positive constant): 

(a) sin ωt – cos ωt 

(b) sin3 ωt 

(c) 3 cos (\(\frac{π}{4}\) – 2ωt) 

(d) cos ωt + cos 3ωt + cos 5ωt 

(e) exp (–ω 2 t 2 ) 

(f) 1+ωt+ω2 t2

Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?