a 0.75 kg mass attached to avertical spring streches the spring 0.30m. what is the spring constant? the mass-spring system is now placed on the horizontal surface and set vibrating. what is the period of the vibration?

k= 24.525n/m

t= 1.098s

bihh hn

@drwls dnt kno nun

Oh, so we have a mass and a spring having a little dance, huh? Let's find that spring constant first!

Using Hooke's Law (F = -kx), where F is the force, k is the spring constant, and x is the displacement, we can find the spring constant:

F = -kx

Plugging in the values, we have:

k = -F / x

Now, in this case, the mass is creating a gravitational force, which can be calculated using Newton's second law (F = mg), where m is the mass and g is the acceleration due to gravity. Since the spring is vertical, we're only concerned with the vertical force:

F = mg = (0.75 kg)(9.8 m/s²) = 7.35 N

Now, we can find the spring constant:

k = -F / x = -7.35 N / 0.30 m = -24.5 N/m

But since we're dealing with a spring constant, which doesn't have a negative value, the spring constant is 24.5 N/m.

Now time for the vibration's period!

The period of a vibrating mass-spring system can be calculated using the formula:

T = 2π√(m / k)

Plugging in the values, we get:

T = 2π√(0.75 kg / 24.5 N/m)
T = 2π√(0.0306 kg/N)
T ≈ 0.98 seconds

So, the period of the vibration is approximately 0.98 seconds. Time to get your groove on, Mr. Mass and Ms. Spring!

To find the spring constant, you can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

Hooke's Law is mathematically represented as F = -kx, where:
- F is the force exerted by the spring,
- k is the spring constant, and
- x is the displacement of the spring from its equilibrium position.

In this case, the mass attached to the vertical spring stretches it by 0.30 m. We can use this information to find the spring constant.

First, let's calculate the force exerted by the spring using the formula F = kx.

Given:
mass (m) = 0.75 kg,
displacement (x) = 0.30 m.

Using F = kx, we get:
F = k * x
k = F / x

Here, F is the force exerted by the spring, which can be calculated using the formula F = m * g, where g is the acceleration due to gravity.

Assuming g is approximately 9.8 m/s²:

F = m * g
F = 0.75 kg * 9.8 m/s²
F ≈ 7.35 N

Now, we can substitute the values of F and x into the equation for k:

k = F / x
k = 7.35 N / 0.30 m
k ≈ 24.5 N/m

Therefore, the spring constant (k) is approximately 24.5 N/m.

Now let's move on to the second part of the question, finding the period of vibration.

The period (T) of a mass-spring system is given by the formula:

T = 2π * √(m / k)

Given:
mass (m) = 0.75 kg,
spring constant (k) ≈ 24.5 N/m.

Now we can calculate the period using these values:

T = 2π * √(m / k)
T = 2π * √(0.75 kg / 24.5 N/m)

Substituting the values:

T = 2π * √(0.03061)
T ≈ 2π * 0.175
T ≈ 1.10 s

Therefore, the period of vibration (T) for the given mass-spring system on a horizontal surface is approximately 1.10 seconds.

k = F/(deflection) = M*g/(0.30 m)

= ___ N/m

P = 2 pi sqrt(M/k) = ____ seconds

Changing from vertical to horizontal vibration does not change the period in a frictionless situation. There might however be more friction when vibrating horizontally, and this makes the period slightly larger. To make an estimate, you would need to know the friction coefficient. They probably expect you to neglect friction