A0.650 kg block is attached to a spring with spring constant 18.0 n/m . while the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 47.0 cm/s . what are
the amplitude of the subsequent oscillations? answer is in cm
the block's speed at the point where x= 0.350 a? answer is in cm/s

amplitude is 8.92 cm

speed of block is 44.11 cm/s

Explanation:

given data

mass = 0.650 kg

spring constant = 18 N/m

speed = 47 cm/s = 0.44 m/s

speed at x point = 0.350 A

to find out

amplitude of subsequent oscillation

solution

we know here conservation of energy

maximum kinetic energy = maximum potential energy

here we know k is spring constant and m is mass and A is amplitude and v is velocity

so solve it we get

A =

put here all these value

A =  

A = 0.08931 m

so amplitude is 8.92 cm

and

by conservation of energy

initial energy = final energy

=

solve we gey V

V =    

put here value Vm = 0.47 , and x = 0.350

V =

V = 0.4411 m/s

so speed of block is 44.11 cm/s

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.