Two springs have their force constant in the ratio of 3 is to 4

https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)%2F13%253A_Simple_Harmonic_Motion%2F13.02%253A_Vertical_spring-mass_system \( \newcommand\] This is the same equation as that for the simple harmonic motion of a horizontal spring-mass system ( Equation 13.1.2), but with the origin located at the equilibrium position instead of at the rest length of the spring. In other words, a vertical spring-mass system will undergo simple harmonic motion in the vertical direction about the equilibrium position. In general, a spring-mass system will undergo simple harmonic motion if a constant force that is co-linear with the spring force is exerted on the mass (in this case, gravity). That motion will be centered about a point of equilibrium where the net force on the mass is zero rather than where the spring is at its rest position. Exercise \(\PageIndex\) How does the period of motion of a vertical spring-mass system compare to the period of a horizontal system (assuming the mass and spring constant are the same)? • The period of the vertical system will be larger. • The period of the vertical system will be smaller. • The period will be the same. Answer Two-spring-mass system Consider a horizontal spring-mass system composed of a single mass, \(m\), attached to two different springs with spring constants \...

CONCEPT: When a spring is stretched by length 'x', potential energy stored in it is given by: \(U = \) So the correct answer is option 2.

Consider a mass m with a spring on either end, each attached to a wall. Let and be the x results in the first spring lengthening by a distance x (and pulling in the direction), while the second spring is compressed by a distance x (and pushes in the same direction). The equation of motion then becomes

AP Physics B Exam 7 Oscillations INTRODUCTION In this chapter, we”ll concentrate on a kind of periodic motion that”s straightforward and that, fortunately, actually describes many real-life systems. This type of motion is called simple harmonic motion. The prototypical example of simple harmonic motion is a block that”s oscillating on the end of a spring, and what we learn about this simple system, we can apply to many other oscillating systems. SIMPLE HARMONIC MOTION (SHM): THE SPRING-BLOCK OSCILLATOR When a spring is compressed or stretched from its natural length, a force is created. For most, but not all, springs, if the spring is displaced by x from its natural length, the force it exerts in response is given by the equation F S = – k x This is known as Hooke”s Law. The proportionality constant, k, is a positive number called the spring (or force) constant that indicates how stiff the spring is. The stiffer the spring, the greater the value of k. The minus sign in Hooke”s Law tells us that F S and x always point in opposite directions. For example, referring to the figure below, when the spring is stretched ( x is to the right), the spring pulls back ( F is to the left); when the spring is compressed ( x is to the left), the spring pushes outward ( F is to the right). In all cases, the spring wants to return to its original length. As a result, the spring tries to restore the attached block to the equilibrium position, which is the position at which the net force on t...