A displacement-time graph plots an object’s displacement on the vertical axis and time on the horizontal axis. In Principles of Physics III, it is a main way to read simple harmonic motion and other oscillations.
A displacement-time graph is the graph you use in Principles of Physics III to show how an object’s position changes over time. The vertical axis is displacement, usually measured from an equilibrium or starting point, and the horizontal axis is time.
The main thing to read on this graph is the slope. A steeper slope means a larger velocity, because displacement is changing faster. A positive slope means the object is moving in the positive direction, a negative slope means it is moving in the opposite direction, and a flat slope means the object is momentarily at rest.
For simple harmonic motion, the graph is usually sinusoidal, meaning it looks like a sine or cosine wave. That shape matches motion where the object keeps swinging back and forth around equilibrium, like a mass on a spring. The curve crosses the time axis when the object passes through equilibrium, and the peaks and valleys show the maximum displacement from that point.
You can also read timing information from the graph. One full cycle from a peak to the next peak is the period, and the number of cycles per second is the frequency. Bigger peaks mean larger amplitude, which tells you how far the system moves away from equilibrium.
The graph does more than show where the object is. It shows how the motion is changing moment by moment. That is why it is so useful in oscillations, because the shape of the curve connects position, velocity, period, and amplitude all in one picture.
A displacement-time graph is one of the fastest ways to describe oscillating motion without writing out every position by hand. In Principles of Physics III, you use it to move between the visual picture of a vibrating system and the math that describes it.
If you are studying simple harmonic motion, this graph lets you spot whether the motion is periodic, how large the oscillations are, and how long each cycle takes. That matters when you later work with phase, frequency, and energy in systems like springs, pendulums, and mechanical vibrations.
It also helps you catch motion mistakes quickly. For example, if the graph is flat, the object is not moving at that moment. If the slope changes sign, the object has switched direction. If a curve is shifted left or right, that can signal a phase difference compared with another oscillator.
A lot of physics questions ask you to interpret the shape of the graph instead of just plugging into a formula. Being able to read a displacement-time graph means you can describe motion in words, estimate velocity from slope, and recognize the pattern of a repeating system before you get to the algebra.
Keep studying Principles of Physics III Unit 1
Visual cheatsheet
view galleryAmplitude
Amplitude is the maximum displacement shown on the graph, measured from equilibrium to a crest or trough. On a displacement-time graph, bigger amplitude means the object swings farther from its center position. That does not tell you how fast it is moving by itself, but it does show the size of the oscillation.
Period
The period is the time for one full repeat of the motion on the graph. You find it by measuring the horizontal distance between matching points, like one peak to the next peak. In oscillation problems, period tells you how long one cycle takes, which is different from how high the graph reaches.
Frequency
Frequency is how many cycles happen each second, so it is the inverse of period. On a displacement-time graph, a motion with more tightly packed waves has a higher frequency. This makes it easy to compare two oscillators, even before you calculate anything.
Phase Angle
Phase angle tells you where in its cycle the motion starts, which changes the graph’s horizontal shift. Two displacement-time graphs can have the same amplitude and period but still be out of step. That difference shows up as one wave leading or lagging the other.
A quiz or problem set will usually ask you to read the graph rather than just name it. You might be asked to identify where the object is moving fastest, where it is at rest, or where it crosses equilibrium. If the graph is sinusoidal, you may also need to find amplitude, period, or frequency from the picture.
A common task is to connect the graph to velocity. Since slope gives velocity, you can use steepness and sign to describe motion at a specific time. Another common move is comparing two graphs to see which oscillator has the larger amplitude, shorter period, or different phase. When you see a graph question, focus on the shape first, then translate that shape into motion words and numbers.
A displacement-time graph shows position as time passes, while a velocity-time graph shows how velocity changes. On a displacement-time graph, slope gives velocity. On a velocity-time graph, the vertical value is already velocity, so the graph means something different even when the motion looks similar.
A displacement-time graph plots displacement on the vertical axis and time on the horizontal axis.
The slope of the graph gives velocity, so steep sections mean faster motion and flat sections mean the object is momentarily at rest.
In simple harmonic motion, the graph usually looks like a sine or cosine wave because the object moves back and forth around equilibrium.
The highest and lowest points show maximum displacement, which is the amplitude of the oscillation.
The spacing between repeating points on the graph shows the period, and the inverse of period gives the frequency.
It is a graph that shows an object’s displacement over time. In this course, you use it to read oscillations, especially simple harmonic motion, where the graph often looks like a sine or cosine wave.
Velocity is the slope of the graph at a given point. A steeper slope means a larger velocity, a positive slope means motion in the positive direction, and a negative slope means motion in the opposite direction.
No. A displacement-time graph shows position versus time, while a velocity-time graph shows velocity versus time. The big clue is that slope means velocity on a displacement-time graph, but the graph’s vertical value is velocity on a velocity-time graph.
It usually means the object is in simple harmonic motion or another repeating oscillation. The peaks and troughs show the turning points, and the graph crossing equilibrium shows the object passing through the center position.