 Let's solve a question where we have to analyze energy for an oscillator from a data table. For this one we have a block which is attached to an ideal spring which oscillates without friction on a horizontal table. A student makes the following measurements on the block. So we have the measurement of spring constant, mass that is 0.5 kg, amplitude, maximum speed and average speed. What is the maximum energy of the block spring system? And we need to choose one answer out of these four options. As always pause the video and first try this one on your own. Alright, hopefully you have given this a shot. Now first let's try to visualize how this system looks like, how the mass spring system looks like. So we can say that there is a block, there is a spring and we can assume that the surface is horizontal and it's frictionless. And the block, the block oscillates, it oscillates like this. We can say that this position in the middle that is the origin, zero position. So the displacement to the left of it, it's negative displacement to the right of it, it's positive. An amplitude is given to us which is 0.3 meters. So when the block oscillates like this, it goes to a maximum positive displacement and this one is 0.3 meters and then when it goes back, goes back then the maximum negative displacement that is minus 0.3, minus 0.3 meters. Alright, what else do we know? We know the spring constant, we know the constant of this spring. This is 80 Newton per meters and we also know the maximum speed 4 meters per second and the mass of the block which is 0.5. So maximum speed really is achieved when the block crosses the equilibrium position when there is no net force acting on the block, the block moves with a maximum speed when it crosses the zero position, the origin over here, the equilibrium position. Now we need to figure out the maximum energy of this block spring system. So first let's try to think about what all forms of energy are even present. Now the block is moving, there is some velocity, so there must be some kinetic energy and we also see a spring in the system. So there must also be an elastic potential energy. There is a kinetic energy, there is also an elastic potential energy. We need to think about the maximum energy. So both, so maximum kinetic and maximum elastic potential energy. And if we think about the maximum kinetic energy, well kinetic energy was half m v square. So maximum k will be achieved when velocity is maximum and maximum elastic potential energy, this should be achieved. This is really half k x square. This will be achieved when x extension is maximum and extension is maximum at two positions that is at two extreme positions, maximum negative and maximum positive. So x will really be the amplitude, this is the amplitude. So the maximum energy of the block spring system, this is half m v max square plus half k k a square. All right, now let's put in the values. We can take half common, mass is 0.5. So 0.5 into v max square which is 16 4 square plus k is 80 into amplitude square that will be 0.09. a square, this will be 0.09. And when you multiply 80 with 0.09, you get 7.2. So you are adding 7.2 here. 0.5 into 16 that is 8 and 8 plus 7.2 that is 15.2 that is 15.2. Now we're dividing 15.2 with 2, 15.2 divided by 2. So this comes out to be equal to 7.6 joules, 7.6 joules and that is that is the last option option b. You can try more questions from this exercise in the lesson and if you're watching on YouTube, do check out the exercise link which is added in the description.