- #1
nukeman
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Homework Statement
Here is the question:
Homework Equations
The Attempt at a Solution
I know that SHM is: accel = -(constant) (displacement)
Linear from my book says: Ax = Ftotal/m (dont quite get this)
Any help? THanks!
technician said:In each case I think the force on the block is 2kx (x is the displacement)
I would use this to write an expression for the acceleration (= F/m)
then acc =ω^2x to get an expression for ω^2 then get the time period expression.
get back to me if you cannot do this
technician said:So if the force = 2kx then acceleration = F/m = 2kx/m
Acceleration = ω^2 x
so ω^2 = 2k/m
Can you get an expression for frequency or time period from this?
ask if you are not sure... but you know the 'rules' of this place... I prefer not to give you the answer directly... you are almost there.
technician said:you have got it
well done
The spring constant, also known as the force constant or stiffness, is a measure of the stiffness of a spring. It is determined by dividing the force applied to the spring by the distance the spring is stretched or compressed.
The formula for calculating the period of oscillation for a spring-mass system is T = 2π√(m/k), where T is the period, m is the mass of the object attached to the spring, and k is the spring constant.
The spring constant directly affects the frequency of oscillation and the amplitude of the oscillations of a spring-mass system. A higher spring constant results in a higher frequency and smaller amplitude, while a lower spring constant results in a lower frequency and larger amplitude.
Simple harmonic motion is when a system oscillates back and forth with a constant amplitude and frequency. Damped harmonic motion is when the amplitude of the oscillations decreases over time due to an external force, such as friction or air resistance.
The length of the spring affects the frequency of oscillation, but not the amplitude. A longer spring will have a lower frequency and a shorter spring will have a higher frequency. However, the spring constant remains the same regardless of the length of the spring.