Aspring-mass system with k1 and m has a natural frequency of ωn. if a second spring k2 is added in series with the first spring, the natural frequency is lowered to 1/2*wn. determine k2 in terms of k1.

Explanation:

When only one spring is connected with mass

When another spring is added in series with spring one ,then the equivalent spring constant is K

Given that final natural frequency become half

       -----(1)

We know that equivalent spring constant for series connection is given as

    -----(2)

By using equation 1 and 2 we can say that

the equation above shows how temperature f, measured in degrees fahrenheit, relates to a temperature c, measured in degrees celsius. based on the equation, which of the following must be true?

a temperature increase of 1 degree fahrenheit is equivalent to a temperature increase of

5

9

degree celsius.

a temperature increase of 1 degree celsius is equivalent to a temperature increase of 1.8 degrees fahrenheit.

a temperature increase of

5

9

degree fahrenheit is equivalent to a temperature increase of 1 degree celsius.

a) i only

b) ii only

c) iii only

d) i and ii only