Simple Harmonic Motion

Equation of a plane progressive wave is given by y = 0.6 sin 2π(t – x/2). On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is

Q: Equation of a plane progressive wave is given by y = 0.6 sin 2π(t – x/2). On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is

(a) y = 0.6 sin 2π(t + x/2)

(b) y = – 0.4 sin 2π(t + x/2)

(c) y = 0.4 sin 2π(t + x/2)

(d) y = – 0.4 sin 2π(t – x/2)

Ans: (b)

A body of mass m is situated in a potential field U(x) = U_0 (1 – cos⁡αx) when, U_0 and α are constants. Find the time period of small oscillations.

Q: A body of mass m is situated in a potential field U(x) = U_0 (1 – cos⁡αx) when, U_0 and α are constants. Find the time period of small oscillations.

A body is performing SHM, then its

Q: A body is performing SHM, then its

(a) Average total energy per cycle is equal to its maximum kinetic energy

(b) Average kinetic energy per cycle is equal to half of its maximum kinetic energy

(c) Mean velocity over a complete cycle is equal to 2/π times of it maximum velocity

(d) Root mean square velocity is 1/√2 times of its maximum velocity

Ans: (a) , (b) & (d)

Which of the following statement is/are true for a simple harmonic oscillator ?

Q: Which of the following statement is/are true for a simple harmonic oscillator ?

(a) Force acting is directly proportional to displacement from the mean position and opposite to it

(b) Motion is periodic

(c) Acceleration of the oscillator is constant

(d) The velocity is periodic

Ans: (a) , (b) & (d)

Displacement versus time curve for a particle executing SHM is shown in figure. Choose the correct statements.

Q: Displacement versus time curve for a particle executing SHM is shown in figure. Choose the correct statements.

Numerical

(a) Phase of the oscillator is same at t = 0 s and t = 2 s

(b) Phase of the oscillator is same at t = 2 s and t = 6 s

(c) Phase of the oscillator is same at t = 1 s and t = 7 s

(d) Phase of the oscillator is same at t = 1 s and t = 5 s

Ans: (b) & (d)