A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s. How much mass must be added to the object to change the period to 2.00 s

The mass added to the object to change the period to 2.00 s is 0.389 kg and this can be determined by using the formula of the time period.

Given :

A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s.

The formula of the time period is given by:

  ---- (1)

where m is the mass and K is the spring constant.

The new time period is given by:

  ---- (2)

where m' is the total mass after the addition and K is the spring constant.

Now, divide equation (1) by equation (2).

Now, substitute the known terms in the above expression.

Simplify the above expression in order to determine the value of m'.

m' = 0.889 Kg

Now, the mass added to the object to change the period to 2.00 s is given by:

m" = 0.889 - 0.500

m" = 0.389 Kg

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389 kg

Explanation:

The computation of mass is shown below:-

Where K indicates spring constant

m indicates mass

For the new time period

Now, we will take 2 ratios of the time period

= 0.889 kg

Since mass to be sum that is

= 0.889 - 0.500

0.389 kg

or

= 389 kg

Therefore for computing the mass we simply applied the above formula.

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