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azamat
3 years ago
11

A 0.750-kg object hanging from a vertical spring is observed to oscillate with a period of 1.50 s. When the 0.750-kg object is r

emoved and replaced by a 1.50-kg object, what will be the period of oscillation
Physics
1 answer:
lawyer [7]3 years ago
3 0

Answer:

New time period, T_2=2.12\ s

Explanation:

Given that,

Mass of the object 1, m_1=0.75\ kg

Time period, T_1=1.5\ s

If object 1 is replaced by object 2, m_2=1.5\ kg

Let T_2 is the new period of oscillation.

The time period of oscillation of mass 1 is given by :

T_1=2\pi \sqrt{\dfrac{m_1}{k}}

1.5=2\pi \sqrt{\dfrac{0.75}{k}}............(1)

The time period of oscillation of mass 2 is given by :

T_2=2\pi \sqrt{\dfrac{m_2}{k}}

T_2=2\pi \sqrt{\dfrac{1.5}{k}}............(2)

From equation (1) and (2) we get :

(\dfrac{T_1}{T_2})^2=\dfrac{m_1}{m_2}

(\dfrac{1.5}{T_2})^2=\dfrac{0.75}{1.5}

\dfrac{1.5}{T_2}=0.707

T_2=2.12\ s

So, the new period of oscillation is 2.12 seconds. Hence, this is the required solution.

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