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A mass attached to a spring oscillates with a period of 44 sec. After 33 kg are​ added, the period becomes 55 sec. Assuming that we can neglect any damping or external​ forces, determine how much mass was originally attached to the spring.

Respuesta :

Answer:

The mass originally attached to the spring was 58.665 kg

Step-by-step explanation:

To solve for this we need to consider the equation for a springs oscillating period:

T = [tex]2*\pi *\sqrt{\frac{m}{k} }[/tex]

Here, m = mass of spring

k = spring constant

Since we know that the period increases by 11 (55 - 44) after the extra weight is added, we have the following equations:

[tex]2*\pi *\sqrt{\frac{m}{k} }=44[/tex]    -Equation 1

[tex]2*\pi *\sqrt{\frac{m+33}{k} }=55[/tex]    -Equation 2

solving both equation simultaneously we get:

m =  58.665 kg

Step-by-step explanation:

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