Question

A tray of mass M = 10 kg is supported on two identical springs, each of spring constant k, as shown in figure. When the tray is depressed a little and released, it executes simple harmonic motion of period 1.5 s. When a block of mass m is placed on the tray, the period of oscillation becomes 3s. The value of m is

• A. 10 kg
• B. 20 kg
• C. 30 kg
• D. 40 kg

Answer 1

Answer: (C)

30 kg

Answer 2

As the two identical springs are connected in parallel.

$\therefore$ The effective spring constant of the combination is

$\therefore \mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { M } } { \mathrm { k } ^ { \prime } } } = 2 \pi \sqrt { \frac { \mathrm { M } } { 2 \mathrm { k } } }$ … (i)

When a block of mass m is placed in the tray the period of oscillations becomes

$\mathrm { T } ^ { \prime } = 2 \pi \sqrt { \frac { \mathrm { M } + \mathrm { m } } { \mathrm { k } ^ { \prime } } } = 2 \pi \sqrt { \frac { \mathrm { M } + \mathrm { m } } { 2 \mathrm { k } } }$ ….. (ii)

Divide (ii) by (i), we get

Squaring both sides we get