Question

A mass m at the end of a spring oscillates with a frequency of 0.83 Hz . When an additional 730 gmass is added to m, the frequency is 0.65 Hz . What is the value of m? Express answer using two sig figs. I have one try left on my physics assignment to get this correct. I have tried 1.158, 1.16(in case it was picky), .88, 1.53, and .90

Answer 1

Concepts and reason

The concept used to solve this problem is frequency of a mass-spring system.

Initially, use the frequency of spring-mass system to obtain the expression for mass.

Finally, use the two frequencies to find the value of .

Fundamentals

The time period of a mass–spring system is given below:

Here, is the spring constant and mass is .

The frequency is given by the inverse of time period as follows:

The initial frequency of the spring mass system is as follows:

…… (1)

The frequency of the spring mass system after the mass of the block increased by is as follows:

Here, new mass is .

Replace by .

…… (2)

Divide and square Equations (1) and (2) as follows:

The ratio of frequencies is as follows:

Substitute for and for .

Rearrange as follows:

Ans:

The value of is .