Suppose I have a spring. I add a mass (m = 1.0 kg) and it is displaced by 15 cm. What is the spring constant k in units of (N/m)?
Force=kx
mg=kx
k=mg/x
A spring mass system mounted horizontally is allowed to oscillates in SHM with a mass of 600g attached to the free end of the spring. A force of 8 N causes 35 mm displacement of the spring. Find: a. free constant of the spring. b. angular frequency period and frequency of the oscillation of the spring. c. suppose the spring is given an initial displacement and velocity of 17mm and 450mm/s. Respectively, find the amplitude. d. Write the equations as functions of time for: position equation, velocity equation, acceleration equation. e. Find the maximum velocity and acceleration of the oscillation.
To calculate the spring constant (k) in units of Newton per meter (N/m), we can use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
The formula for Hooke's Law is:
F = -k * x
Where:
F is the force applied by the spring (in N),
k is the spring constant (in N/m),
x is the displacement of the spring (in m).
Given that the mass (m) is 1.0 kg and the displacement (x) is 15 cm (or 0.15 m), we can use the equation F = m * g to calculate the force applied by the mass:
F = m * g
F = 1.0 kg * 9.8 m/s^2
F = 9.8 N
Now, we can rearrange the equation F = -k * x to solve for k:
k = -F / x
k = -9.8 N / 0.15 m
k ≈ -65.33 N/m
The negative sign in front of the spring constant indicates the direction of the force exerted by the spring. In this case, it implies that the spring force opposes the displacement of the spring.
Therefore, the spring constant (k) is approximately 65.33 N/m, with a negative sign indicating the direction of the force.