The motion of the mass starting from its highest point t=1.3

In summary, the conversation is about a large spring with a mass of 30 kg attached to a platform and set into vertical oscillations. In part a), the stiffness (spring constant) is determined to be 705.6 N/m, and the amplitude of the motion is calculated to be 0.24 m. In part b), the question asks for the distance traveled by the mass in 1.3 s, given that the motion is timed from the highest point. The formula x= A cos (wt) is suggested to be used, with t=1.3 s. However, the answer does not match the expected 0.88 m, possibly due to the calculator not being set to radians. It is suggested
  • #1
Marisabel
2
0

Homework Statement


(a) A large spring has one end attached to the floor and a platform attached to its upper end. On the platform is placed a mass of 30 kg. The mass of the platform itself is 10kg. The spring-platform-mass system is then set into vertical oscillations with a period of 1.5 s. Determine

(i) the stiffness (spring constant) of the spring
(ii) the amplitude of the motion if the maximum speed of the mass is 1 ms-1.
(b) (i) If the motion of the mass (in part (a)) is timed starting from its highest point, calculate how far it has traveled in 1.3 s

Homework Equations


x= A cos (wt)

The Attempt at a Solution


The answer must be x= 0.88m

I've solved part a) already
k= 705.6 N/m
w= 4.2 rad/s
A= 0.24 m

but I'm struggling in part b)
Can someone help me using the formula
x= A cos (wt)PS: This is a past exam paper, I'm using it to study and practice for my exam.
 
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  • #2
Marisabel said:

Homework Statement


(a) A large spring has one end attached to the floor and a platform attached to its upper end. On the platform is placed a mass of 30 kg. The mass of the platform itself is 10kg. The spring-platform-mass system is then set into vertical oscillations with a period of 1.5 s. Determine

(i) the stiffness (spring constant) of the spring
(ii) the amplitude of the motion if the maximum speed of the mass is 1 ms-1.
(b) (i) If the motion of the mass (in part (a)) is timed starting from its highest point, calculate how far it has traveled in 1.3 s

Homework Equations


x= A cos (wt)

The Attempt at a Solution


The answer must be x= 0.88m

I've solved part a) already
k= 705.6 N/m
w= 4.2 rad/s
A= 0.24 m

but I'm struggling in part b)
Can someone help me using the formula
x= A cos (wt)PS: This is a past exam paper, I'm using it to study and practice for my exam.

Did you think about plugging ##t = 1.3s## into that equation?
 
  • #3
PeroK said:
Did you think about plugging ##t = 1.3s## into that equation?
yes. I get a different answer.
 
  • #4
Try plugging in ##t = 0s## and ##t=1.5s## and see if that gives you any ideas.
 
  • #5
What is x at t=0? And what is x at t=1.3 s? What is the displacement during that time?
By the way, have you set the calculator to radians?
 

1. What is the initial position and velocity of the mass at t=1.3?

The initial position of the mass is its highest point, where the displacement is 0. The initial velocity is 0, since the mass is momentarily at rest at t=1.3.

2. How does the mass move after t=1.3?

The motion of the mass after t=1.3 depends on the forces acting on it. If there are no external forces, the mass will continue to move in a straight line with constant velocity. If there are external forces, the mass may accelerate, decelerate, or change direction.

3. What factors affect the motion of the mass at t=1.3?

The motion of the mass at t=1.3 can be affected by various factors such as the initial position and velocity, external forces (such as gravity or friction), and the mass of the object itself. Other factors like air resistance and surface conditions may also impact the motion.

4. Can the motion of the mass at t=1.3 be predicted?

The motion of the mass at t=1.3 can be predicted using mathematical equations such as Newton's laws of motion or the equations of motion for a specific scenario. However, external factors and uncertainties may affect the accuracy of the prediction.

5. How does the motion of the mass at t=1.3 relate to its potential and kinetic energy?

At t=1.3, the mass is at its highest point and has no kinetic energy, only potential energy. As it starts to move, its potential energy decreases while its kinetic energy increases. The relationship between potential and kinetic energy is described by the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred between different forms.

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