Question

A mass rests on a frictionless surface and is attached to the end of a spring. The mass is pulled so that the spring is stretched...

I would appreciate to have a detailed explanation for the last one. Thank you in advance.

A mass rests on a frictionless surface and is attached to the end of a spring. The mass is pulled so that the spring Is stretched. The mass Is then released, and It starts oscillating back and forth In simple harmonic motion. We'll definet0 when the oscillating mass is released. The position of the mass at any time is descrihed by x(t) (4.3 cm)cos(7.3 rad/s)r Determine the following (a) frequency of the motion 1.16 (b) period of the motion 030 (c) amplitude of the motion Cm (d) first time after t 0 that the object reaches the positionx 2.6 cm. Note that in this case, you can't do any "tricks" to find the time; i.e. it won't be some simple fraction of the periad. You will need to set x(t)-2.6 cm and then solve for t. Given an expression for the position of an oscillating mass at any time, how can we determine the time that the mass is at a particular position? s

Answer 1

d] here x(t) = 2.6

4.3 * cos 7.3t = 2.6

cos 7.3t = 2.6/4.3

7.3t = arccos (2.6/4.3) = 0.9215

t = 0.9215/7.3

= 0.1262s answer