Weird performance of a linear servo

[mamech]

Hello

I want to make a servo motor to move in sine wave motion. I believe that the code should be very easy, but strangely, the results are not as I expected.
first thing, I decided to use timer1 (the target is Arduino Uno) :

#include <Servo.h>
#include <TimerOne.h>            //Timer number one library
double t = 0;
float y = 0;
float f = 0.2; // frequency, and changing it will change speed of actuation
const double pi = 3.141593;
double w = 2 * pi * f;
float c = 0;   // phase shift
float d = 0;   // offset
float a = 10;  // max position amplitude
float resolution = 80;   // sine function number of samples per cycle
Servo myservo, myservo1, myservo2;  // create servo object to control a servo
boolean flag = false;
float sample_step;

float val = 0;   // variable to read the value from the analog pin
int i = 0;
void setup()
{
  myservo.attach(9);  // attaches the servo on pin 9 to the servo object
  myservo1.attach(10);  // attaches the servo on pin 10 to the servo object
  myservo2.attach(11);  // attaches the servo on pin 11 to the servo object
  Serial.begin(115200);
  sample_step = (1 / f) * 1000 / resolution;
  myservo.writeMicroseconds(1000);
  myservo1.writeMicroseconds(1000);
  myservo2.writeMicroseconds(1000);
  delay(3000);
  myservo.writeMicroseconds(1500);
  myservo1.writeMicroseconds(1500);
  myservo2.writeMicroseconds(1500);
  delay(3000);
}



void loop()
{

  y = a * sin(w * t + c) + d;
  y=y*100;
  int k = map(y, -1500, 1500, 1000, 2000);//(y + 10) * 100;
  myservo.writeMicroseconds(k);
  myservo1.writeMicroseconds(k);
  myservo2.writeMicroseconds(k);
  Serial.print(k);
  Serial.print("  ");
  Serial.println(t);
  while (i < sample_step)
  {
    delay(1);
    i++;
  }
  i = 0;
  t = t + (1 / f) / resolution;
}

The servo did not work at all. I believe that there is a problem in conflict between timer1 and servo library.
so I changed the code to be delay based.

#include <Servo.h>
#include <TimerOne.h>            //Timer number one library
double t = 0;
float y = 0;
float f = 0.2; // frequency, and changing it will change speed of actuation
const double pi = 3.141593;
double w = 2 * pi * f;
float c = 0;   // phase shift
float d = 0;   // offset
float a = 10;  // max position amplitude
float resolution = 80;   // sine function number of samples per cycle, do not exceed 1000
Servo myservo, myservo1, myservo2;  // create servo object to control a servo
boolean flag = false;
float sample_step;

float val = 0;   // variable to read the value from the analog pin
int i = 0;
void setup()
{
  myservo.attach(9);  // attaches the servo on pin 9 to the servo object
  myservo1.attach(10);  // attaches the servo on pin 10 to the servo object
  myservo2.attach(11);  // attaches the servo on pin 11 to the servo object
  Serial.begin(115200);
  sample_step = (1 / f) * 1000 / resolution;
  myservo.writeMicroseconds(1000);
  myservo1.writeMicroseconds(1000);
  myservo2.writeMicroseconds(1000);
  delay(3000);
  myservo.writeMicroseconds(1500);
  myservo1.writeMicroseconds(1500);
  myservo2.writeMicroseconds(1500);
  delay(3000);
}



void loop()
{

  y = a * sin(w * t + c) + d;
  y=y*100;
  int k = map(y, -1500, 1500, 1000, 2000);//(y + 10) * 100;
  myservo.writeMicroseconds(k);
  myservo1.writeMicroseconds(k);
  myservo2.writeMicroseconds(k);
  Serial.print(k);
  Serial.print("  ");
  Serial.println(t);
  while (i < sample_step)
  {
    delay(1);
    i++;
  }
  i = 0;
  t = t + (1 / f) / resolution;
}

this code worked, but this resulted in sluggish performance (motion is not smooth):
https://www.youtube.com/watch?v=m0AEOE2SOuY&feature=youtu.be

in the video only one motor is connected

what is wrong in my code? any suggestions?