Simple harmonic motion equation form

[sam1212]

Homework Statement

what is the form of the equation of motion for the SHM of a mass suspended on a spring when the mass is initially (a)released 10 cm above the equilibrium position; (b) given an upward push from the equilibrium position, so that it undergoes a maximum displacement of 8cm; (c) given a downward push from the equilibrium position, so that it undergoes a maximum displacement of 12 cm?

Homework Equations

So I know y= Acos(t*2*pi)/T

The Attempt at a Solution

so would (a) just be y = .10cos t/[square root(m/k)]

 

[alphysicist]

Homework Statement

what is the form of the equation of motion for the SHM of a mass suspended on a spring when the mass is initially (a)released 10 cm above the equilibrium position; (b) given an upward push from the equilibrium position, so that it undergoes a maximum displacement of 8cm; (c) given a downward push from the equilibrium position, so that it undergoes a maximum displacement of 12 cm?

Homework Equations

So I know y= Acos(t*2*pi)/T

The Attempt at a Solution

so would (a) just be y = .10cos t/[square root(m/k)]

That looks right to me; you can change the square root and move it around if you like, though (to get it out of the denominator), but since they don't tell you anything about the spring I'm guessing they don't care about how you write the argument of the cosine function.

 

[nlightner]

?

The general equation for simple harmonic motion is y = A*cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. In this case, the mass suspended on a spring is undergoing simple harmonic motion, so we can use this equation to describe its motion.

(a) When the mass is released 10 cm above the equilibrium position, it has an initial displacement of 10 cm, which means A = 10 cm. The angular frequency, ω, is given by ω = 2π/T, where T is the period of the motion. Since the mass is suspended on a spring, the period can be calculated using T = 2π√(m/k), where m is the mass and k is the spring constant. So the equation of motion for (a) would be y = 10*cos(2πt/√(m/k)).

(b) When the mass is given an upward push and undergoes a maximum displacement of 8 cm, we can determine that the amplitude is now 8 cm. The rest of the equation remains the same, so the equation of motion for (b) would be y = 8*cos(2πt/√(m/k)).

(c) Similarly, when the mass is given a downward push and undergoes a maximum displacement of 12 cm, the amplitude becomes 12 cm. The equation of motion for (c) would be y = 12*cos(2πt/√(m/k)).

It's important to note that in all three cases, the period remains the same, as it is solely dependent on the mass and the spring constant. The only thing that changes is the amplitude, which is determined by the initial displacement or the maximum displacement.