Question 3: Oscillations

Question

A tray of mass (M) 12 kg is supported by a spring as shown in the figure.

When the tray is pressed down and released, it executes SHM with a period of 1.5 s. When a block of mass m placed on the tray, the period of SHM changes to 3.0 s. The mass of block is

Accepted Answer

Let k be the force constant of spring.
Time period, $$T = 2\pi \sqrt {{M \over k}} $$ ...... (i)
When block of mass m is placed in the tray, the time period of oscillations becomes
$$T' = 2\pi \sqrt {{{M + m} \over k}} $$ ...... (ii)
On dividing Eq. (ii) by Eq. (i), we get
$$ \Rightarrow {{T'} \over T} = {{\sqrt {M + m} } \over {\sqrt M }}$$
$$ \Rightarrow {3 \over {1.5}} = \sqrt {{{12 + m} \over {12}}} $$ [given, M = 12 kg, T = 1.5 s, T' = 3 s]
$$ \Rightarrow \sqrt {{{12 + m} \over {12}}}  = 2$$
$$\Rightarrow$$ 12 + m = 48
$$\Rightarrow$$ m = 36 kg

Answer

36 kg

Answer

48 kg

Answer

12 kg

Answer

24 kg

Oscillations

A tray of mass (M) 12 kg is supported by a spring as shown in the figure. When the tray is pressed down and released, it executes SHM with a period of 1.5 s. When a block of mass m placed on the tray, the period of SHM changes to 3.0 s. The mass of block is

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