A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it. The natural frequency of this mass-spring system is:

a)0.014
b)5.3Hz
c)31.8Hz
d)181.7Hz
e)need to know M
please explain the answer....and hope to answer soon.... thanks in advance

To find the natural frequency of a mass-spring system, we need to know the mass (M) and the spring constant (k).

Given information:
- The spring elongates 9 mm when it is suspended vertically.
- A block of mass M is hung on the spring.

We are not given the value of M or k, so we cannot directly calculate the natural frequency. Therefore, the correct answer is option e) need to know M.

To calculate the natural frequency (f), we can use the formula:

f = 1 / (2π) * √(k / M)

The spring constant (k) is a measure of the stiffness of the spring and it determines how much force is required to stretch or compress the spring by a certain distance. Without the value of k, we cannot calculate the natural frequency.

Hence, the answer is e) need to know M.

To determine the natural frequency of a mass-spring system, you need to know two things: the mass of the object attached to the spring and the spring constant.

In this case, we are given that the spring elongates 9 mm when a block of mass M is hung on it. However, we don't know the specific value of M. Since the frequency depends on both the mass and the spring constant, we need to know the mass in order to calculate the frequency.

Therefore, the correct answer is option e) "need to know M." Without this information, we cannot determine the natural frequency of the mass-spring system.

no idea