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What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by k1 and k2 as shown below.

1. √((k1 + k2)/(2m))
2. √((k1 + k2)/(4m))
3. √((k1 - k2)/m)
4. √((k1 + k2)/m)

Correct answer: √((k1 + k2)/m)

Solution

The natural frequency of a spring-mass system is determined by the total effective spring constant and the mass. In this case, since the springs are in series, their combined effect leads to the formula √((k1 + k2)/m), which accurately reflects the system's oscillatory behavior.

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