# Plotting a graph of accelleration agains displacement (x)

• Ebies
In summary, the conversation discusses plotting a graph of acceleration against displacement (x) for a mass suspended from a spring. The given values include a mass of 0.3kg and a spring stiffness of 200Nm-1. The frequency of vibration, maximum velocity, maximum acceleration, and mass required to produce double the maximum velocity are also calculated using formulas such as f=1/2∏*√k/m and a=A*ω^2. Assistance is requested for calculating point E), but the person eventually figures it out on their own.
Ebies
Plotting a graph of acceleration agains displacement (x)

A mass of 0.3kg suspended from a spring of stiffness 200Nm-1. If the mass is displaced by 10mm from its equilibrium position and released calculate:

A) frequency of vibration

B) max velocity

C) max acceleration

D) mass required to produce double the maximum velocity but using the same amplitude

E) plot a graph of acceleration against displacement (x) (for values of x from x= -10mm to x= 10mm

A) f=1/2∏*√k/m

B) Vmax=A*ω

C) a=A*ω^2

D) i doubled Vmax then used ω=Vmax/A
Then m=k/ω^2

E) i have no idea

I am not after the answers as such but just a nudge in the right direction, i don't even know where to start on this or what formulae to use... I only need assistance with calculating point E)

Last edited:
Its ok i managed to work it out thanks guys! ;)

## 1. What is the relationship between acceleration and displacement?

The relationship between acceleration and displacement is described by the fundamental equation of motion, which states that acceleration is equal to the second derivative of displacement with respect to time. In simpler terms, acceleration is the rate of change of displacement over time.

## 2. How do you plot a graph of acceleration against displacement?

To plot a graph of acceleration against displacement, you will need to collect data for both variables by conducting experiments or using mathematical equations. Once you have the data, plot acceleration on the y-axis and displacement on the x-axis. Then, connect the data points with a line to visualize the relationship between the two variables.

## 3. What are the units for acceleration and displacement?

The standard units for acceleration are meters per second squared (m/s^2) or feet per second squared (ft/s^2). The standard units for displacement are meters (m) or feet (ft). However, the specific units may vary depending on the context and the system of measurement being used.

## 4. What does a graph of acceleration against displacement tell us?

A graph of acceleration against displacement can provide valuable insights into the motion of an object. It can show the relationship between the two variables, whether it is linear, curved, or non-existent. It can also help us understand the acceleration of the object at different displacement values and can be used to make predictions about its future motion.

## 5. How can we use a graph of acceleration against displacement in real-life situations?

A graph of acceleration against displacement can be used in real-life situations to analyze the motion of objects, such as cars, airplanes, or roller coasters. It can also be used in engineering and design to optimize the performance of machines and structures. Additionally, it can help us understand the forces acting on an object and how they affect its motion.

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