Simple harmonic motion is a cyclic or periodic motion in which the further the object moves from its position of equilibrium, the greater the force that pulls it back to where it originally started. If the graph is curved, the speed of the object must have changed because the slope has changed. Here, the slope of the graph will provide you with information about an object's speed. In a distance versus time graph, you'll find the distance on the y-axis and time on the x-axis. The area under a force-time graph is force multiplied by time, or a quantity called impulse, which is equal to the change in an object's momentum. Area is more important than the slope on a force versus time graph. In a force versus time graph, you'll find force on the y-axis and time on the x-axis. Calculating the area is similar to multiplying the y-variable by the x-variable, while calculating the slope is like dividing them. Graphs can help you calculate slope and area. This speeding up and slowing down creates a sine curve.Ī distance-time graph for simple harmonic motion is a sine shape. As the spring stretches, it moves towards its limit, then gets slower, stops, and springs back again. Imagine a spring bouncing back and forth and you'll see why. In relation to simple harmonic motion both force-time and distance-time graphs have a sinusoidal shape or that of a sine curve. Classic examples of simple harmonic motion include masses on springs and pendulums. Simple harmonic motion is a periodic or cyclic motion, where the further the object moves from its position of equilibrium, the greater the force that pulls it back to its starting point. If the graph is curved and the slope is changing, that means the speed of the cart must also have changed. The slope of a distance versus time graph tells you the speed, or how fast the shopping cart is moving. In this case, the slope, rather than the area, is what's important. This type of a graph would allow you to measure how far that same shopping cart moves around the supermarket as it is being pushed. So you can figure out how much the momentum changes by finding the area under a force-time graph.Ī distance versus time graph is a graph that shows distance on the y-axis and time on the x-axis. Impulse is equal to the change in momentum of an object. The area under a force-time graph is force multiplied by time, which is a quantity called impulse. With a force-time graph, the slope isn't important however, area is important. For example, you might plot the force applied to a shopping cart over time as it's pushed across the supermarket. time graph is a graph that shows force on the y-axis and time on the x-axis. You can use this approach for any equation and graph, such as force-time and distance-time graphs.Ī force vs. And if you know that resistance equals voltage divided by current, you can use a graph that shows voltage on the y-axis and current on the x-axis, and the slope will give you the resistance. And, when you calculate the area, it's like taking the value on the y-axis and multiplying it by the value on the x-axis.įor instance, if you know that voltage equals current multiplied by resistance, and you have a graph of current against resistance, you can find the area under the graph, which will tell you the voltage. When you calculate the slope, it's like taking the value on the y-axis and dividing it by the value on the x-axis. But, did you know that graphs can also be used to figure out important numbers?įor example, you can use a graph to calculate the slope, as well as the area under the graph. In math, graphs are especially useful because they can turn numbers into pictures. Some people love numbers, but numbers aren't always the best way to get a good picture of a situation.
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