A 0.300- kg brass block is attached to a spring of negligible mass. What is the value of the spring constant if the vibrational frequency is 0.855Hz?

The spring constant can be calculated using the equation k = (4π^2mf^2)/g, where m is the mass of the block, f is the frequency, and g is the acceleration due to gravity (9.81 m/s^2). Therefore, the spring constant is k = (4π^2*0.300 kg*(0.855 Hz)^2)/9.81 m/s^2 = 0.945 N/m.

To find the value of the spring constant, we can use the formula for the vibrational frequency of a mass-spring system:

f = 1/ (2π) * √(k / m)

Where:
f is the vibrational frequency
k is the spring constant
m is the mass of the block

Given:
m = 0.300 kg
f = 0.855 Hz

Rearranging the formula to solve for k, we get:

k = (4π² * m * f²)

Substituting the given values into the formula:

k = (4π² * 0.300 kg * (0.855 Hz)²)

Calculating the value:

k ≈ 16.113 N/m

Therefore, the value of the spring constant is approximately 16.113 N/m.

To find the value of the spring constant, we need to use the formula for the vibrational frequency of a mass-spring system:

f = 1 / (2π) * √(k / m)

Where:
- f is the vibrational frequency in Hz
- k is the spring constant in N/m (newtons per meter)
- m is the mass of the block in kg

In this case, we are given the vibrational frequency (f = 0.855 Hz) and the mass (m = 0.300 kg). We can rearrange the formula to solve for the spring constant (k):

k = (4π² * m * f²)

Now, we can substitute the known values into the equation:

k = (4π² * 0.300 kg * (0.855 Hz)²)

To calculate this, we can use a calculator or a math software tool:

k ≈ 33.456 N/m

Therefore, the value of the spring constant is approximately 33.456 N/m.