Chapter 10
SIMPLE HARMONIC MOTION
PREVIEW
An object such as a pendulum or a mass on a spring is oscillating or vibrating if it is moving in a repeated path at regular time intervals. We call this type of motion harmonic motion. For an object to continue oscillating there must be a restoring force continually trying to restore it to its equilibrium position. For, the force exerted by an ideal spring obeys Hooke’s law. As an object in simple harmonic motion oscillates, its energy is repeatedly converted from potential energy to kinetic energy, and vice – versa.
The content contained in sections 1, 2, 3, and 4 of chapter 10 of the textbook is included on the AP Physics B exam.
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Important Terms
amplitude
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For an ideal spring, the stretch is proportional to the force, but in the opposite direction. If we pull with twice the force, the spring will stretch twice as far.
The graph below represents the magnitude of the force F vs stretched length x for a spring:
The slope of the line is the change in force (rise) divided by the change in length (run). Since this ratio is also equal to the spring constant k, the higher slope of the graph the higher the spring constant, which is an indication of the stiffness of the spring.
We can find the spring constant k for this spring by taking the ratio of the force to the stretch for a particular interval. In other words, we can find the slope of the F vs. x graph for each spring. The slope of the line and the spring constant for spring is 50 N/m.
As on any other F vs. x graph, the work done in stretching or compressing the spring to a certain displacement can be found by finding the area under the graph. The total work done in stretching this spring is
10.2 Simple Harmonic Motion and the Reference Circle
In the equation for the spring force above, x is the displacement from equilibrium position at any time. Because of the oscillatory nature of the vibrating mass, we can express the displacement x from equilibrium position at any time t as or where A is the amplitude of oscillation and (the lower case Greek
than they would at their natural length. This means that the muscle fibers will generate less tension with each
First, we will set up the force table. The table comes in three separate pieces the base, stand and table once we connect and fasten all three parts we must use a circular level to make sure the table is balanced. If the force table isn’t balanced then we must adjust the base’s feet to the appropriate levels on each leg till the bubble on the level is centered. We must then assign where the positive & negative x, y axis are on the force table as a point of reference and label them with tape .Then for part I we must apply 1.96 N in the positive x – direction, and 2.94 N in the positive y-direction then we must balance the two with a third force and record the magnitude and direction of it and a draw a diagram showing all three forces. Part II
During an eccentric contraction, the muscle lengthens under tension due to an opposing force that is greater than the force being produced by the muscle (Lindstedt et al. 2001). Eccentric contractions require little metabolic energy, however they are characterized by a high production of force (Semmler 2014). Fick observed that a lengthening muscle contraction could exert more force than a shortening muscle contraction, while Hill later observed that the body has a lower energy demand when contracting eccentrically compared to concentrically (Lindstedt et al. 2001). When the force applied is larger than the force that is created, work is done on the lengthened muscle and mechanical energy is absorbed – this is called “negative work” (Lindstedt et al. 2001). This absorbed energy can either be dissipated as heat, or it can be temporarily stored as elastic recoil potential energy for later use (Lindstedt et al. 2001).
3. What happens to the total force as the muscle length is increased from 50mm to 100 mm?
The average rate of change is an average slope from the initial point to the final point. We would have to use A(x)=f(x)-f(a) divided by x-a to find the average rate of change. Sometimes we would want to know what the average rate of change is in the middle of the graph. The average rate of change is used in page 10, “How many more people?.” The concept of slope comes from the idea of a constant rate of change. To find the slope, you have to calculate y1-y2 divided by x1-x2. Slope is often denoted by the letter “m” which means that m+ equals the slope. Its problem is being used in page 21, “Rates, Graph, Slopes, and Equations.” Y=mx+b is the equation of the line that you can find using the two points. Variable “m” is the slope and “b” is the y-intercept.
The further the muscle is stretched the bigger the force it exerts. This is a linear effect.
Throughout the world there are many religious beliefs. Religion has been existing for a very long time, even before christ, religions serve as a worship to a “god.” There are different perspectives on how one sees religion, even though all religions tend to have similarities they all have a branch that that guides them to a different path than the rest and makes them unique. As Joseph Campbell said, “your sacred space is where you can find yourself again and again.” (Campbell, 158-print). He meant that one does not have to follow someone else’s beliefs if one is not happy with what one is worshipping. Campbell emphasizes the fact that every religion is a way to express the human feelings towards a certain god or a thing of either an ancient civilization or a current one. Every generation and tribes have had different systems of beliefs. Take for example “Buddhism” which is a religion that began in the seventh century, before christ” (Religion, Funk and wagnalls- online). It is a very popular religion that has been going on for many centuries with more than 300 million followers. “Christianity is currently the world’s number one religion, and just like Buddhism they both worship some type of God” (Religion, Funk and wagnalls- online). Others religions are based on mythology, because humans do not have many information on whether that “religion” was real or not. Greek mythology is an
As a professional health care worker, the implication confidentiality breach regarding ethical dilemmas are significant to nurse and patient. The information disclosed can cause problems on a personal and professional level. Breach of confidentiality occurs when the heath care work discloses the patient 's medical or personal information without the patient 's informed written or verbal consent. Confidentiality is needed between the nurse and the patient to maintain a good open and honest relationship between both parties. There are several ethical implications regarding breach of confidentiality, for example,
Use a protractor to measure 30° from the equilibrium. Release the pendulum at this angle.
The strength of a muscle is proportional to the surface area of its cross section.
Explanation: This all happens because of the formula, Force = Mass X Acceleration. So physically when extra mass is added, the force will increase (e.g. 20 N = 2/m^2 x 10 Kg > 10 N = 2/m^2 x 5 Kg)
The more stimuli per second, the greater the force generated by the muscle due to a
Gas lighting. Re-writing history. Manipulation of society and facts. One might think these were being used to describe current political climates. However, these describe the methods and rhetoric used by Squealer, the talking pig, in George Orwell’s Animal Farm, in his quest for the pig’s complete control over the farm. Squealer, like a true politician, lies and takes advantage of the less intelligent and informed animals on the farm to ensure he and the pigs have all the power.
Below are two tables in which I have recorded the data which I obtained during the experiment. The first table reflects the Relationship between the deflection/flexion of the cantilever and the mass of the load and the second table reflects the relationship between the flexion of the cantilever and the length of the cantilever.
Following tables and graphs show the result of the experiment. The tables will demonstrate the experimental and theoretical deflection for each case. The graphs will show the relationship between the load applied and deflection, in addition to compare the experimental deflection and theoretical deflection.