Oscillating mechanical systems. find maximum velocity and acceleration ?

In summary, a mass of 0.3 kg suspended from a spring with a stiffness of 200 N m–1 and a displacement of 10 mm will result in vibrations with a maximum velocity of 0.2582 m/s and a maximum acceleration of 6.6667 m/s^2. To double the maximum velocity, the required mass would be 0.15 kg.
  • #1
bensm0
20
0
Oscillating mechanical systems. find maximum velocity and acceleration !?

A mass of 0.3 kg is suspended from a spring of stiffness 200 N m–1. If the mass is displaced by 10 mm from its equilibrium position and released, for the resulting vibration

A) Calculate maximum velocity
B) Calculate maximum acceleration

I need help with this please, for starters is the amplitude 0.01m?

Thanks
 
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  • #2


Yes, amplitude is correct, you must have had some training :smile:. Welcome to PF. There are a ton of googleable resources out there. Check them out, give the problem a try and come back with some specific questions.
 
  • #3


Ok thanks

I think I've got it now

using:-

v=- ωA sin(ωt - φ)
a= - ω2A cos(ωt - φ)

And the maximums occur when sin(ωt - φ)=1 and cos(ωt - φ)=1

Thanks again!
 
  • #5


omega = square root (k/m) = 25.82

a) 0.001 x 25.82 x 1 = 0.2582 m/s

b)0.001 x 25.82^2 x 1 = 6.6667 m/s^2

Anybody care to have a go at the last question:-

d) the mass required to produce double the maximum velocity
calculated in (b) using the same spring and initial deflection

I get an answer of 0.075kg

Thanks
 
  • #6
bensm0 said:
omega = square root (k/m) = 25.82

a) 0.001 x 25.82 x 1 = 0.2582 m/s

b)0.001 x 25.82^2 x 1 = 6.6667 m/s^2

Anybody care to have a go at the last question:-

d) the mass required to produce double the maximum velocity
calculated in (b) using the same spring and initial deflection

I get an answer of 0.075kg

Thanks

would this not be 0.15kg?

ω = √k/m = 200/0.15 = 36.51

b)0.001 x 36.51^2 x 1 = 13.33 m/s^2 = double Vmax

I know this is a late response to a question but i have the same question and want to check my working.

(thanks in advance)
 
  • #7
Eddievic,

I got the same answers as bensm0,

If you double the answer that you got in a) 0.5164
use that in your equations and transpose for mass.

i think :)
 
  • #8
justadaftspark said:
Eddievic,

I got the same answers as bensm0,

If you double the answer that you got in a) 0.5164
use that in your equations and transpose for mass.

i think :)

I believe you are correct my paper came back and mine was incorrect the paper was an overall pass though so I have not investigated it fully.
 

1. How do you define an oscillating mechanical system?

An oscillating mechanical system is a physical system that exhibits periodic motion or vibrations around a stable equilibrium point. This can include systems such as a pendulum, a spring-mass system, or a simple harmonic oscillator.

2. What factors affect the maximum velocity and acceleration of an oscillating mechanical system?

The maximum velocity and acceleration of an oscillating mechanical system are affected by a variety of factors, including the amplitude of the oscillation, the mass of the object, and the stiffness of the system. Other factors such as damping and external forces can also have an impact.

3. How is maximum velocity and acceleration calculated in an oscillating mechanical system?

The maximum velocity and acceleration in an oscillating mechanical system can be calculated using the equations v = ωA and a = -ω²A, where ω is the angular frequency and A is the amplitude of the oscillation. These equations are derived from the equations of motion for simple harmonic motion.

4. What is the relationship between maximum velocity and acceleration in an oscillating mechanical system?

In an oscillating mechanical system, the maximum velocity and acceleration are directly related. This means that as the maximum velocity increases, the maximum acceleration also increases, and vice versa. This relationship can be seen in the equations v = ωA and a = -ω²A, where ω is constant for a given system.

5. How can the maximum velocity and acceleration of an oscillating mechanical system be measured?

The maximum velocity and acceleration of an oscillating mechanical system can be measured using various instruments such as accelerometers or motion sensors. These devices can be attached to the system and used to record the oscillations, allowing for the calculation of maximum velocity and acceleration. Alternatively, these values can also be calculated using mathematical equations and known parameters of the system.

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