Match the following entries in column-I and column-II with respect to an oscillating spring-block system:

Column-I		Column-II
(a)	Mass of the block is doubled	(i)	Energy of oscillation becomes 4 times
(b)	Spring constant is made 4 times	(ii)	Speed of block becomes 2 times
(c)	Amplitude of oscillations is doubled	(iii)	P.E. becomes 4 times
(d)	Angular frequency is doubled	(iv)	Time period becomes √2 times
(e)	length of spring is quadrupled	(v)	Time period becomes 2 times

Concept:

• A spring-block oscillator is where you hang a block of mass m on a vertically hanging spring, stretch it, and then let it bounce back and forth. This bouncing is an example of simple harmonic motion.

• Time period =  --- (1)
• The total energy,  --- (2)
• The potential energy of spring  --- (3)
• For a particle undergoing simple Harmonic Motion, maximum velocity is given by v = A × ω --- (4)
  • Where A = amplitude

Calculation:

From equation 1

• T ∝ √ m, if the mass of the block is doubled then, time period becomes √2 times.

From equation 3

• P.E. ∝ K, if Spring constant is made 4 times then, P.E. becomes 4 times

From equation 4

• v ∝ A, if Amplitude of oscillations is doubled then, Speed of block becomes 2 times.

From equation 2

• E ∝ ω², if Angular frequency is doubled then, Energy of oscillation becomes 4 times.