Question

Block 1 is attached to a spring and oscillates on a horizontal frictionless surface. When block 1 is at a point of maximum displacement, block 2 is placed on top of it from directly above without interrupting the oscillation, and the two blocks stick together. How do the maximum kinetic energy and period of oscillation with both blocks compare to those of block 1 alone?

Max KE Period
a) Smaller Greater
b) Smaller Smaller
c) The Same Greater
d) The Same Smaller

Answer 1

D

Step-by-step explanation:

Suppose mass of block 1 is and of block 2

For original system

natural frequency of oscillation is given by

Maximum kinetic Energy is equal to total Energy of the system

where k=spring constant

A=maximum amplitude

Now Block B is Placed at block 1 at maximum amplitude such that A=A'

i.e. new amplitude=old amplitude

Maximum kinetic energy of combined system is

as the total energy is independent of mass therefore maximum kinetic energy will remain same

Answer 2

d) The Same Smaller

Step-by-step explanation:

When block 2 is placed on top of block 1, the total mass of the system increases but the amplitude of the oscillation remains the same. Since the total energy of the system is conserved, the maximum kinetic energy of the system must remain the same as that of block 1 alone. However, the period of the oscillation will be smaller with both blocks than with block 1 alone because the mass of the system has increased, and the period of a simple harmonic oscillator is inversely proportional to the square root of the mass.