Iteration for A Level Maths: staircase method & cobweb method

E.g. f(x) = x² - x - 4 When the above is rearranged in the form of x = g(x), it is said to be in iterative form. x² - x - 4 = 0 x = 1 + x/4 x n+1 = 1 + x n / 4 If x n is known, x n+1 can be calculated. The initial value to trigger off the iterative process is found by looking for change in sign of…

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Simple Harmonic Motion for A Level Physics: vertical motion of a spring

Upward force, T', when the stretched spring is released = k(e+x) If the resultant force is F, F = K(e+x) -mg F = ma - Newton's Second Law k(e+x) - mg = ma, where a is the acceleration (ke + kx) - mg = ma Since T = ke mg - mg + kx = ma ma = kx a = k/m x a ∝ x ω 2  = k/m T =2π √(m/k) T =2π √(m/k) Since the a…

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Mechanics - A Level Applied Maths & Physics: really challenging questions

An object that falls off a tree travels 16/25 th of the height of the tree during the last second. Assuming that g = 10 m/s², find the total time taken for the fall and the height of the tree. A balloon is steadily rising at 5 m/s. After 4 seconds of its motion, a nail from the balloon falls off. Sk…

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Simple Harmonic Motion for A Level Physics: proof of motion of simple pendulum being SHM

As you can see, when the weight of the pendulum bob is resolved, the tension of the string,  T , and the  mg cos x  cancel each other out, leaving  mg sin x  as the net force, as shown above. This force is responsible for bringing the bob down in a curved path. Using F = ma for the bob, mg sin x = ma, wher…

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